| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 1.1-a1 |
1.1-a |
$1$ |
$1$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$3.31111$ |
$\textsf{none}$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3$ |
3Nn |
$1$ |
\( 1 \) |
$0.053983237$ |
$242.2485520$ |
1.058780902 |
\( -268 a^{2} - 964 a - 281 \) |
\( \bigl[a\) , \( a - 1\) , \( a^{2} - a - 5\) , \( 96 a^{2} - 233 a - 196\) , \( -1883 a^{2} + 4595 a + 3857\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(96a^{2}-233a-196\right){x}-1883a^{2}+4595a+3857$ |
| 2.1-a1 |
2.1-a |
$2$ |
$3$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{24} \) |
$3.71660$ |
$(-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.136233792$ |
$56.53568258$ |
1.247163719 |
\( \frac{158856620125}{16777216} a^{2} - \frac{105234107615}{16777216} a - \frac{1201897809843}{16777216} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - 6\) , \( a + 1\) , \( 1472705 a^{2} - 980825 a - 11115626\) , \( -1788123223 a^{2} + 1166528817 a + 13571910454\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(1472705a^{2}-980825a-11115626\right){x}-1788123223a^{2}+1166528817a+13571910454$ |
| 2.1-a2 |
2.1-a |
$2$ |
$3$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{8} \) |
$3.71660$ |
$(-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.408701377$ |
$18.84522752$ |
1.247163719 |
\( -\frac{1483205075}{256} a^{2} - \frac{4598406095}{256} a - \frac{2391517923}{256} \) |
\( \bigl[1\) , \( a^{2} - a - 6\) , \( 1\) , \( -17 a^{2} + 11 a + 129\) , \( -19 a^{2} + 14 a + 139\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-17a^{2}+11a+129\right){x}-19a^{2}+14a+139$ |
| 2.1-b1 |
2.1-b |
$2$ |
$2$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{3} \) |
$3.71660$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$0.402892806$ |
$186.3181470$ |
1.519394902 |
\( -\frac{139}{8} a^{2} - \frac{5415}{8} a + \frac{18125}{8} \) |
\( \bigl[a^{2} - 4\) , \( -1\) , \( a^{2} - 5\) , \( a^{2} - 7\) , \( -4 a^{2} - 15 a - 13\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}-{x}^{2}+\left(a^{2}-7\right){x}-4a^{2}-15a-13$ |
| 2.1-b2 |
2.1-b |
$2$ |
$2$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{6} \) |
$3.71660$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$0.201446403$ |
$186.3181470$ |
1.519394902 |
\( -\frac{179685}{64} a^{2} + \frac{747063}{64} a + \frac{2936555}{64} \) |
\( \bigl[1\) , \( a\) , \( a + 1\) , \( a^{2} - a - 6\) , \( -a^{2} + 5\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(a^{2}-a-6\right){x}-a^{2}+5$ |
| 2.1-c1 |
2.1-c |
$1$ |
$1$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{12} \) |
$3.71660$ |
$(-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$9.384542945$ |
3.039198761 |
\( -\frac{7553506099}{4096} a^{2} + \frac{18426974289}{4096} a + \frac{15477051837}{4096} \) |
\( \bigl[1\) , \( a^{2} - 6\) , \( a^{2} - a - 5\) , \( -23 a^{2} - 64 a - 21\) , \( -572 a^{2} - 1777 a - 934\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-23a^{2}-64a-21\right){x}-572a^{2}-1777a-934$ |
| 2.1-d1 |
2.1-d |
$2$ |
$2$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{2} \) |
$3.71660$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.140309776$ |
$163.9652994$ |
0.931313439 |
\( \frac{10062257397771}{4} a^{2} + \frac{31197344743347}{4} a + \frac{16227186293807}{4} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 2 a + 6\) , \( a^{2} - 5\) , \( 64 a^{2} - 39 a - 472\) , \( 651 a^{2} - 424 a - 4910\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(64a^{2}-39a-472\right){x}+651a^{2}-424a-4910$ |
| 2.1-d2 |
2.1-d |
$2$ |
$2$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( -2 \) |
$3.71660$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.280619553$ |
$163.9652994$ |
0.931313439 |
\( -\frac{185396353}{2} a^{2} + \frac{119842765}{2} a + \frac{1396112431}{2} \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 5\) , \( a^{2} - 4\) , \( -6 a - 7\) , \( 2 a^{2} - 14\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(-6a-7\right){x}+2a^{2}-14$ |
| 3.1-a1 |
3.1-a |
$6$ |
$8$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{6} \) |
$3.97644$ |
$(a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3Nn |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$290.6705566$ |
2.941690930 |
\( \frac{208834000}{729} a^{2} - \frac{507492800}{729} a - \frac{425032063}{729} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 5\) , \( a + 1\) , \( 272 a^{2} - 178 a - 2045\) , \( 2295 a^{2} - 1513 a - 17344\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(272a^{2}-178a-2045\right){x}+2295a^{2}-1513a-17344$ |
| 3.1-a2 |
3.1-a |
$6$ |
$8$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{3} \) |
$3.97644$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 3 \) |
$1$ |
$145.3352783$ |
2.941690930 |
\( \frac{21779882311970}{27} a^{2} - \frac{53126963527870}{27} a - \frac{44642867263373}{27} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 5\) , \( a + 1\) , \( -893 a^{2} + 592 a + 6765\) , \( 17491 a^{2} - 11560 a - 132272\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-893a^{2}+592a+6765\right){x}+17491a^{2}-11560a-132272$ |
| 3.1-a3 |
3.1-a |
$6$ |
$8$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{6} \) |
$3.97644$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$72.66763917$ |
2.941690930 |
\( -\frac{244223477098}{729} a^{2} + \frac{164283341012}{729} a + \frac{1853927757439}{729} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 185307491 a^{2} - 122510546 a - 1401465717\) , \( -2511173901522 a^{2} + 1660188078601 a + 18991807148142\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(185307491a^{2}-122510546a-1401465717\right){x}-2511173901522a^{2}+1660188078601a+18991807148142$ |
| 3.1-a4 |
3.1-a |
$6$ |
$8$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{3} \) |
$3.97644$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 3 \) |
$1$ |
$145.3352783$ |
2.941690930 |
\( -\frac{9464222}{27} a^{2} + \frac{6262570}{27} a + \frac{71562557}{27} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 3 a^{2} - a - 22\) , \( 4 a^{2} - a - 28\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3a^{2}-a-22\right){x}+4a^{2}-a-28$ |
| 3.1-a5 |
3.1-a |
$6$ |
$8$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{12} \) |
$3.97644$ |
$(a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3Nn |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$145.3352783$ |
2.941690930 |
\( -\frac{3550635884}{531441} a^{2} + \frac{2622778300}{531441} a + \frac{28879042673}{531441} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 5\) , \( 1\) , \( 153515 a^{2} - 101494 a - 1161015\) , \( -58943750 a^{2} + 38968909 a + 445786866\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(153515a^{2}-101494a-1161015\right){x}-58943750a^{2}+38968909a+445786866$ |
| 3.1-a6 |
3.1-a |
$6$ |
$8$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{24} \) |
$3.97644$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$18.16690979$ |
2.941690930 |
\( \frac{1216173909380578}{282429536481} a^{2} - \frac{2934026733078188}{282429536481} a - \frac{2471299669401919}{282429536481} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 5\) , \( 1\) , \( -8755 a^{2} + 5786 a + 66220\) , \( -176808360 a^{2} + 116891597 a + 1337187474\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-8755a^{2}+5786a+66220\right){x}-176808360a^{2}+116891597a+1337187474$ |
| 4.1-a1 |
4.1-a |
$1$ |
$1$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{2} \) |
$4.17174$ |
$(a^2-a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.243864844$ |
$90.25450260$ |
1.781985068 |
\( -\frac{77615}{2} a^{2} + \frac{189191}{2} a + 79687 \) |
\( \bigl[a^{2} - 4\) , \( 1\) , \( 1\) , \( -a^{2} + 4 a + 16\) , \( -2 a^{2} + 7 a + 29\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-a^{2}+4a+16\right){x}-2a^{2}+7a+29$ |
| 4.1-b1 |
4.1-b |
$1$ |
$1$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{8} \) |
$4.17174$ |
$(a^2-a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.058476575$ |
$64.80992372$ |
0.613676400 |
\( \frac{11663}{16} a^{2} + \frac{12099}{16} a - \frac{74739}{8} \) |
\( \bigl[a^{2} - 4\) , \( 1\) , \( a^{2} - a - 5\) , \( a^{2} + 4 a + 1\) , \( a^{2} + 4 a + 1\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+{x}^{2}+\left(a^{2}+4a+1\right){x}+a^{2}+4a+1$ |
| 5.1-a1 |
5.1-a |
$1$ |
$1$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
5.1 |
\( 5 \) |
\( 5^{3} \) |
$4.32981$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$0.047780762$ |
$352.4439823$ |
1.363418429 |
\( \frac{3887104}{125} a^{2} + \frac{2445312}{25} a + \frac{6381568}{125} \) |
\( \bigl[0\) , \( -a\) , \( 1\) , \( 2 a - 3\) , \( -4 a^{2} + a + 34\bigr] \) |
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(2a-3\right){x}-4a^{2}+a+34$ |
| 6.1-a1 |
6.1-a |
$4$ |
$4$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{5} \cdot 3^{12} \) |
$4.46340$ |
$(-a-1), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$23.76149786$ |
1.923799467 |
\( -\frac{84674124006775}{17006112} a^{2} + \frac{47838829275485}{17006112} a + \frac{667541293160857}{17006112} \) |
\( \bigl[a^{2} - 4\) , \( 1\) , \( a + 1\) , \( 2796 a^{2} - 1616 a - 21852\) , \( 159717 a^{2} - 102273 a - 1218196\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(2796a^{2}-1616a-21852\right){x}+159717a^{2}-102273a-1218196$ |
| 6.1-a2 |
6.1-a |
$4$ |
$4$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{10} \cdot 3^{6} \) |
$4.46340$ |
$(-a-1), (a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$95.04599146$ |
1.923799467 |
\( -\frac{489678725}{746496} a^{2} + \frac{236250775}{746496} a + \frac{5380791563}{746496} \) |
\( \bigl[a^{2} - 4\) , \( 1\) , \( a + 1\) , \( 181 a^{2} - 101 a - 1412\) , \( 2491 a^{2} - 1598 a - 18969\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(181a^{2}-101a-1412\right){x}+2491a^{2}-1598a-18969$ |
| 6.1-a3 |
6.1-a |
$4$ |
$4$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{5} \cdot 3^{3} \) |
$4.46340$ |
$(-a-1), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$95.04599146$ |
1.923799467 |
\( \frac{31738525}{864} a^{2} + \frac{102513025}{864} a + \frac{62204717}{864} \) |
\( \bigl[a\) , \( -a^{2} + a + 6\) , \( a\) , \( 7 a^{2} - 19 a - 12\) , \( -22 a^{2} + 53 a + 45\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(7a^{2}-19a-12\right){x}-22a^{2}+53a+45$ |
| 6.1-a4 |
6.1-a |
$4$ |
$4$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{20} \cdot 3^{3} \) |
$4.46340$ |
$(-a-1), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$47.52299573$ |
1.923799467 |
\( \frac{123846379225}{28311552} a^{2} - \frac{292533613235}{28311552} a - \frac{238685443063}{28311552} \) |
\( \bigl[1\) , \( -a^{2} + a + 6\) , \( 1\) , \( -24497 a^{2} + 16223 a + 185183\) , \( 8073936 a^{2} - 5337993 a - 61062067\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-24497a^{2}+16223a+185183\right){x}+8073936a^{2}-5337993a-61062067$ |
| 8.1-a1 |
8.1-a |
$2$ |
$3$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{38} \) |
$4.68262$ |
$(-a-1), (a^2-a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$5.703610052$ |
3.694245890 |
\( -\frac{13270480126465}{16777216} a^{2} - \frac{41152787030933}{16777216} a - \frac{21395464557233}{16777216} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 5\) , \( a^{2} - 5\) , \( -1322409 a^{2} - 4100032 a - 2132604\) , \( -2673502049 a^{2} - 8289011260 a - 4311499254\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-1322409a^{2}-4100032a-2132604\right){x}-2673502049a^{2}-8289011260a-4311499254$ |
| 8.1-a2 |
8.1-a |
$2$ |
$3$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{50} \) |
$4.68262$ |
$(-a-1), (a^2-a-7)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2^{3} \) |
$1$ |
$17.11083015$ |
3.694245890 |
\( \frac{49862757355}{2097152} a^{2} - \frac{22991818599}{2097152} a - \frac{12750951223}{65536} \) |
\( \bigl[a\) , \( a^{2} - a - 6\) , \( 0\) , \( -96 a^{2} + 345 a - 144\) , \( 1684 a^{2} - 5176 a - 139\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-96a^{2}+345a-144\right){x}+1684a^{2}-5176a-139$ |
| 8.1-b1 |
8.1-b |
$4$ |
$6$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{54} \) |
$4.68262$ |
$(-a-1), (a^2-a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$7.889206698$ |
0.638732950 |
\( \frac{4701355597620603}{4398046511104} a^{2} + \frac{17397561280017303}{4398046511104} a + \frac{19210877901126155}{4398046511104} \) |
\( \bigl[a^{2} - 4\) , \( a\) , \( 0\) , \( 5412 a^{2} - 3611 a - 40788\) , \( 189736 a^{2} - 125231 a - 1435552\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}={x}^{3}+a{x}^{2}+\left(5412a^{2}-3611a-40788\right){x}+189736a^{2}-125231a-1435552$ |
| 8.1-b2 |
8.1-b |
$4$ |
$6$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{18} \) |
$4.68262$ |
$(-a-1), (a^2-a-7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$213.0085808$ |
0.638732950 |
\( -\frac{35605348389}{16384} a^{2} + \frac{23884483959}{16384} a + \frac{270089553515}{16384} \) |
\( \bigl[a^{2} - 4\) , \( a\) , \( 0\) , \( 2667 a^{2} - 1751 a - 20168\) , \( -134942 a^{2} + 89205 a + 1020629\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}={x}^{3}+a{x}^{2}+\left(2667a^{2}-1751a-20168\right){x}-134942a^{2}+89205a+1020629$ |
| 8.1-b3 |
8.1-b |
$4$ |
$6$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{45} \) |
$4.68262$ |
$(-a-1), (a^2-a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$7.889206698$ |
0.638732950 |
\( -\frac{540411886627}{2097152} a^{2} + \frac{356265149601}{2097152} a + \frac{4090249012685}{2097152} \) |
\( \bigl[a\) , \( -a + 1\) , \( a^{2} - a - 5\) , \( 30 a^{2} + 33 a - 393\) , \( 322 a^{2} + 101 a - 3409\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(30a^{2}+33a-393\right){x}+322a^{2}+101a-3409$ |
| 8.1-b4 |
8.1-b |
$4$ |
$6$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{15} \) |
$4.68262$ |
$(-a-1), (a^2-a-7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$213.0085808$ |
0.638732950 |
\( \frac{91907957}{128} a^{2} - \frac{224349479}{128} a - \frac{187902515}{128} \) |
\( \bigl[a\) , \( -a + 1\) , \( a^{2} - a - 5\) , \( -10 a^{2} + 28 a + 7\) , \( 37 a^{2} - 92 a - 71\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a^{2}+28a+7\right){x}+37a^{2}-92a-71$ |
| 8.1-c1 |
8.1-c |
$1$ |
$1$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{10} \) |
$4.68262$ |
$(-a-1), (a^2-a-7)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.043720871$ |
$272.2695728$ |
1.927542234 |
\( -\frac{1831}{16} a^{2} - \frac{8445}{16} a - \frac{11371}{16} \) |
\( \bigl[a\) , \( a^{2} - 4\) , \( a^{2} - 5\) , \( -3 a^{2} + 11 a + 9\) , \( 39 a^{2} - 91 a - 79\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-3a^{2}+11a+9\right){x}+39a^{2}-91a-79$ |
| 9.1-a1 |
9.1-a |
$4$ |
$4$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$4.77545$ |
$(-a^2+2a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$221.2118931$ |
1.492496126 |
\( \frac{9574}{3} a^{2} + \frac{26461}{3} a + \frac{13294}{3} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 6\) , \( 1\) , \( -5 a^{2} + 17 a + 16\) , \( 6 a + 3\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-5a^{2}+17a+16\right){x}+6a+3$ |
| 9.1-a2 |
9.1-a |
$4$ |
$4$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{8} \) |
$4.77545$ |
$(-a^2+2a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$55.30297328$ |
1.492496126 |
\( \frac{6394700}{81} a^{2} + \frac{19914587}{81} a + \frac{10527326}{81} \) |
\( \bigl[a\) , \( a^{2} - a - 4\) , \( a^{2} - a - 5\) , \( 19052 a^{2} - 12596 a - 144082\) , \( -865833 a^{2} + 572448 a + 6548142\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(19052a^{2}-12596a-144082\right){x}-865833a^{2}+572448a+6548142$ |
| 9.1-a3 |
9.1-a |
$4$ |
$4$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$4.77545$ |
$(-a^2+2a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$13.82574332$ |
1.492496126 |
\( -\frac{1007222794}{3} a^{2} - \frac{5387845663}{3} a + \frac{26386761968}{3} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 2054 a^{2} - 1002 a - 16632\) , \( 103587 a^{2} - 62567 a - 801761\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2054a^{2}-1002a-16632\right){x}+103587a^{2}-62567a-801761$ |
| 9.1-a4 |
9.1-a |
$4$ |
$4$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$4.77545$ |
$(-a^2+2a+4)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$110.6059465$ |
1.492496126 |
\( -\frac{36223}{9} a^{2} - \frac{145468}{9} a + \frac{818972}{9} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 129 a^{2} - 62 a - 1042\) , \( 1635 a^{2} - 995 a - 12629\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(129a^{2}-62a-1042\right){x}+1635a^{2}-995a-12629$ |
| 9.2-a1 |
9.2-a |
$1$ |
$1$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{6} \) |
$4.77545$ |
$(a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3Nn |
$1$ |
\( 2 \) |
$1$ |
$47.15874531$ |
2.545405446 |
\( -268 a^{2} - 964 a - 281 \) |
\( \bigl[a\) , \( -a^{2} + 6\) , \( a^{2} - 5\) , \( -2 a^{2} - 2 a + 9\) , \( -a^{2} - 2 a + 1\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-2a^{2}-2a+9\right){x}-a^{2}-2a+1$ |
| 9.2-b1 |
9.2-b |
$6$ |
$8$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{12} \) |
$4.77545$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$27.82928727$ |
0.375523240 |
\( -\frac{244223477098}{729} a^{2} + \frac{164283341012}{729} a + \frac{1853927757439}{729} \) |
\( \bigl[a^{2} - 4\) , \( a - 1\) , \( a\) , \( 1252873993 a^{2} - 828300445 a - 9475385676\) , \( 44145663735937 a^{2} - 29185595076418 a - 333870120102590\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1252873993a^{2}-828300445a-9475385676\right){x}+44145663735937a^{2}-29185595076418a-333870120102590$ |
| 9.2-b2 |
9.2-b |
$6$ |
$8$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{9} \) |
$4.77545$ |
$(a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2^{2} \) |
$1$ |
$55.65857455$ |
0.375523240 |
\( -\frac{9464222}{27} a^{2} + \frac{6262570}{27} a + \frac{71562557}{27} \) |
\( \bigl[a^{2} - 4\) , \( a - 1\) , \( a\) , \( 22 a^{2} - 10 a - 156\) , \( -83 a^{2} + 62 a + 640\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(22a^{2}-10a-156\right){x}-83a^{2}+62a+640$ |
| 9.2-b3 |
9.2-b |
$6$ |
$8$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{18} \) |
$4.77545$ |
$(a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3Nn |
$1$ |
\( 2^{2} \) |
$1$ |
$55.65857455$ |
0.375523240 |
\( -\frac{3550635884}{531441} a^{2} + \frac{2622778300}{531441} a + \frac{28879042673}{531441} \) |
\( \bigl[a\) , \( -a^{2} + 6\) , \( a^{2} - a - 4\) , \( 1037916 a^{2} - 686188 a - 7849677\) , \( 1035509725 a^{2} - 684596513 a - 7831477144\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(1037916a^{2}-686188a-7849677\right){x}+1035509725a^{2}-684596513a-7831477144$ |
| 9.2-b4 |
9.2-b |
$6$ |
$8$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{30} \) |
$4.77545$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2^{2} \) |
$1$ |
$13.91464363$ |
0.375523240 |
\( \frac{1216173909380578}{282429536481} a^{2} - \frac{2934026733078188}{282429536481} a - \frac{2471299669401919}{282429536481} \) |
\( \bigl[a\) , \( -a^{2} + 6\) , \( a^{2} - a - 4\) , \( -59204 a^{2} + 39147 a + 447733\) , \( 3108352234 a^{2} - 2054994820 a - 23508219017\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-59204a^{2}+39147a+447733\right){x}+3108352234a^{2}-2054994820a-23508219017$ |
| 9.2-b5 |
9.2-b |
$6$ |
$8$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{12} \) |
$4.77545$ |
$(a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3Nn |
$1$ |
\( 2^{2} \) |
$1$ |
$55.65857455$ |
0.375523240 |
\( \frac{208834000}{729} a^{2} - \frac{507492800}{729} a - \frac{425032063}{729} \) |
\( \bigl[1\) , \( -1\) , \( a^{2} - a - 4\) , \( 1826 a^{2} - 1203 a - 13824\) , \( -41935 a^{2} + 27731 a + 317128\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}-{x}^{2}+\left(1826a^{2}-1203a-13824\right){x}-41935a^{2}+27731a+317128$ |
| 9.2-b6 |
9.2-b |
$6$ |
$8$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{9} \) |
$4.77545$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Nn |
$4$ |
\( 2 \) |
$1$ |
$6.957321819$ |
0.375523240 |
\( \frac{21779882311970}{27} a^{2} - \frac{53126963527870}{27} a - \frac{44642867263373}{27} \) |
\( \bigl[1\) , \( -1\) , \( a^{2} - a - 4\) , \( -6084 a^{2} + 4087 a + 45811\) , \( -302398 a^{2} + 200376 a + 2285601\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}-{x}^{2}+\left(-6084a^{2}+4087a+45811\right){x}-302398a^{2}+200376a+2285601$ |
| 10.1-a1 |
10.1-a |
$1$ |
$1$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{17} \cdot 5^{5} \) |
$4.86005$ |
$(-a-1), (-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$1$ |
$20.74855689$ |
2.799771779 |
\( -\frac{10016207505747}{409600000} a^{2} - \frac{9716709473091}{81920000} a - \frac{27483170112099}{409600000} \) |
\( \bigl[a^{2} - 4\) , \( a - 1\) , \( a\) , \( -43 a^{2} + 29 a + 331\) , \( -406 a^{2} + 260 a + 3048\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-43a^{2}+29a+331\right){x}-406a^{2}+260a+3048$ |
| 10.1-b1 |
10.1-b |
$2$ |
$3$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5 \) |
$4.86005$ |
$(-a-1), (-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.579222854$ |
$56.58404681$ |
2.653540255 |
\( -\frac{17}{10} a^{2} - \frac{5771}{2} a - \frac{19469}{10} \) |
\( \bigl[a\) , \( -a + 1\) , \( a^{2} - a - 5\) , \( -10 a^{2} - 38 a - 21\) , \( -71 a^{2} - 223 a - 120\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a^{2}-38a-21\right){x}-71a^{2}-223a-120$ |
| 10.1-b2 |
10.1-b |
$2$ |
$3$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{3} \cdot 5^{3} \) |
$4.86005$ |
$(-a-1), (-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.193074284$ |
$169.7521404$ |
2.653540255 |
\( \frac{143394013}{1000} a^{2} - \frac{69866811}{200} a - \frac{293587179}{1000} \) |
\( \bigl[1\) , \( a^{2} - a - 6\) , \( 1\) , \( -481 a^{2} + 1139 a + 1092\) , \( 11100 a^{2} - 27929 a - 20109\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-481a^{2}+1139a+1092\right){x}+11100a^{2}-27929a-20109$ |
| 10.1-c1 |
10.1-c |
$4$ |
$4$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{28} \cdot 5^{2} \) |
$4.86005$ |
$(-a-1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$66.43726239$ |
1.792984189 |
\( -\frac{90284798431949}{6710886400} a^{2} + \frac{12497103230243}{1342177280} a + \frac{691790637158467}{6710886400} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + a + 6\) , \( 1\) , \( 33 a^{2} - 20 a - 240\) , \( -113 a^{2} + 76 a + 865\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(33a^{2}-20a-240\right){x}-113a^{2}+76a+865$ |
| 10.1-c2 |
10.1-c |
$4$ |
$4$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{7} \cdot 5^{8} \) |
$4.86005$ |
$(-a-1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$33.21863119$ |
1.792984189 |
\( \frac{23374123938800127859}{50000000} a^{2} + \frac{14493976253492221027}{10000000} a + \frac{37694947022224550403}{50000000} \) |
\( \bigl[a\) , \( -a\) , \( a^{2} - a - 4\) , \( -16 a^{2} - 22 a - 7\) , \( 41 a^{2} + 260 a + 152\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}-a{x}^{2}+\left(-16a^{2}-22a-7\right){x}+41a^{2}+260a+152$ |
| 10.1-c3 |
10.1-c |
$4$ |
$4$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{14} \cdot 5^{4} \) |
$4.86005$ |
$(-a-1), (-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$132.8745247$ |
1.792984189 |
\( \frac{1537958801323}{10240000} a^{2} + \frac{948334222619}{2048000} a + \frac{2482799052091}{10240000} \) |
\( \bigl[a\) , \( -a\) , \( a^{2} - a - 4\) , \( -a^{2} - 2 a - 2\) , \( a^{2} + 4 a\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}-a{x}^{2}+\left(-a^{2}-2a-2\right){x}+a^{2}+4a$ |
| 10.1-c4 |
10.1-c |
$4$ |
$4$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{7} \cdot 5^{2} \) |
$4.86005$ |
$(-a-1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$132.8745247$ |
1.792984189 |
\( \frac{10529505637}{3200} a^{2} - \frac{5311422219}{640} a - \frac{18881843371}{3200} \) |
\( \bigl[1\) , \( a^{2} - 5\) , \( a^{2} - a - 5\) , \( -17 a^{2} - 16 a + 5\) , \( 91 a^{2} + 202 a + 87\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-17a^{2}-16a+5\right){x}+91a^{2}+202a+87$ |
| 10.1-d1 |
10.1-d |
$1$ |
$1$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5 \) |
$4.86005$ |
$(-a-1), (-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$17.51572652$ |
0.472707929 |
\( -\frac{8376939}{10} a^{2} - \frac{5192667}{2} a - \frac{13503483}{10} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - 2 a - 6\) , \( a + 1\) , \( a^{2} - 8 a - 5\) , \( -6 a - 4\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(a^{2}-8a-5\right){x}-6a-4$ |
| 10.1-e1 |
10.1-e |
$1$ |
$1$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{9} \cdot 5^{3} \) |
$4.86005$ |
$(-a-1), (-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3^{3} \) |
$0.005149385$ |
$237.3879531$ |
2.672168577 |
\( \frac{10302287557}{64000} a^{2} - \frac{1382539179}{12800} a - \frac{77971165131}{64000} \) |
\( \bigl[1\) , \( a^{2} - 6\) , \( a\) , \( 4 a^{2} - 2 a - 29\) , \( -21 a^{2} + 14 a + 158\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(4a^{2}-2a-29\right){x}-21a^{2}+14a+158$ |
| 12.1-a1 |
12.1-a |
$2$ |
$2$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{14} \cdot 3^{18} \) |
$5.01000$ |
$(a+2), (a^2-a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$7.866320855$ |
0.955320070 |
\( \frac{2087431689641753}{49589822592} a^{2} - \frac{2078188127984953}{49589822592} a - \frac{563079355904345}{12397455648} \) |
\( \bigl[a\) , \( a^{2} - 2 a - 5\) , \( 0\) , \( -111 a^{2} - 28 a + 610\) , \( 834 a^{2} - 1459 a - 8507\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-111a^{2}-28a+610\right){x}+834a^{2}-1459a-8507$ |
| 12.1-a2 |
12.1-a |
$2$ |
$2$ |
3.3.1373.1 |
$3$ |
$[3, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{28} \cdot 3^{9} \) |
$5.01000$ |
$(a+2), (a^2-a-7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$7.866320855$ |
0.955320070 |
\( -\frac{191921532797}{322486272} a^{2} + \frac{129248924599}{322486272} a + \frac{712500413545}{161243136} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -233 a^{2} - 726 a - 380\) , \( -34313 a^{2} - 106388 a - 55341\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-233a^{2}-726a-380\right){x}-34313a^{2}-106388a-55341$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
