| 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 |
| 3.1-a1 |
3.1-a |
$2$ |
$5$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{2} \) |
$2.33394$ |
$(-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 2 \) |
$1$ |
$0.458569357$ |
1.054252076 |
\( -\frac{44588942472159799443984364}{9} a^{2} - \frac{103894855095349922928862481}{9} a - \frac{19136402750270179594933979}{9} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - 4\) , \( a\) , \( -711 a^{2} - 1648 a - 303\) , \( -25464 a^{2} - 59301 a - 10927\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-711a^{2}-1648a-303\right){x}-25464a^{2}-59301a-10927$ |
| 3.1-a2 |
3.1-a |
$2$ |
$5$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{10} \) |
$2.33394$ |
$(-a-1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$57.32116973$ |
1.054252076 |
\( -\frac{712591111}{59049} a^{2} - \frac{1713781049}{59049} a - \frac{425773469}{59049} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - 4\) , \( a\) , \( -a^{2} - 3 a + 2\) , \( -3 a^{2} - 7 a - 2\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-a^{2}-3a+2\right){x}-3a^{2}-7a-2$ |
| 3.1-b1 |
3.1-b |
$2$ |
$3$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{6} \) |
$2.33394$ |
$(-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.101887038$ |
$30.08154052$ |
0.845550776 |
\( -\frac{45508954}{729} a^{2} + \frac{96551665}{729} a + \frac{22234402}{729} \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{2} - a + 4\) , \( 0\) , \( -21 a^{2} + 42 a + 23\) , \( -106 a^{2} + 221 a + 64\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-21a^{2}+42a+23\right){x}-106a^{2}+221a+64$ |
| 3.1-b2 |
3.1-b |
$2$ |
$3$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{2} \) |
$2.33394$ |
$(-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.033962346$ |
$90.24462157$ |
0.845550776 |
\( \frac{5135}{9} a^{2} - \frac{1964}{9} a - \frac{25028}{9} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( a^{2} - 2 a - 1\) , \( -a^{2} + a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(a^{2}-2a-1\right){x}-a^{2}+a$ |
| 9.1-a1 |
9.1-a |
$2$ |
$2$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{4} \) |
$2.80291$ |
$(a^2-a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$76.97293065$ |
1.769609561 |
\( \frac{1039204454}{3} a^{2} - \frac{6521028671}{9} a - \frac{1441655537}{9} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 4\) , \( a^{2} - 3\) , \( -6 a^{2} - 11 a + 5\) , \( 7 a^{2} + 18 a + 6\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-6a^{2}-11a+5\right){x}+7a^{2}+18a+6$ |
| 9.1-a2 |
9.1-a |
$2$ |
$2$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$2.80291$ |
$(a^2-a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$153.9458613$ |
1.769609561 |
\( -\frac{32573}{3} a^{2} + 13094 a + \frac{70415}{3} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 4\) , \( a^{2} - 3\) , \( -a^{2} - a + 5\) , \( -1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-a^{2}-a+5\right){x}-1$ |
| 9.1-b1 |
9.1-b |
$1$ |
$1$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$2.80291$ |
$(a^2-a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.113350442$ |
$102.7922861$ |
1.607216670 |
\( 84672 a^{2} + \frac{592622}{3} a + \frac{114047}{3} \) |
\( \bigl[a^{2} + a - 3\) , \( 1\) , \( a^{2} - 3\) , \( a + 3\) , \( -a^{2} + 4\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+{x}^{2}+\left(a+3\right){x}-a^{2}+4$ |
| 9.1-c1 |
9.1-c |
$2$ |
$5$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$2.80291$ |
$(a^2-a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$0.412570325$ |
0.474250093 |
\( 172220318165625 a^{2} + \frac{1203670910165626}{3} a + \frac{221342237692873}{3} \) |
\( \bigl[a\) , \( -a\) , \( a^{2} + a - 3\) , \( -461 a^{2} - 1119 a - 321\) , \( -13387 a^{2} - 31390 a - 6263\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}-a{x}^{2}+\left(-461a^{2}-1119a-321\right){x}-13387a^{2}-31390a-6263$ |
| 9.1-c2 |
9.1-c |
$2$ |
$5$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$2.80291$ |
$(a^2-a-4)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$51.57129063$ |
0.474250093 |
\( \frac{16982}{81} a^{2} + \frac{90025}{243} a + \frac{18013}{243} \) |
\( \bigl[a\) , \( -a\) , \( a^{2} + a - 3\) , \( -a^{2} - 4 a - 1\) , \( -2 a - 3\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}-a{x}^{2}+\left(-a^{2}-4a-1\right){x}-2a-3$ |
| 9.2-a1 |
9.2-a |
$2$ |
$3$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{12} \) |
$2.80291$ |
$(-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$14.98533526$ |
1.378052898 |
\( -\frac{45508954}{729} a^{2} + \frac{96551665}{729} a + \frac{22234402}{729} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} - a + 3\) , \( a^{2} + a - 3\) , \( -21 a^{2} + 12 a + 75\) , \( -16 a^{2} + 31 a + 9\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-21a^{2}+12a+75\right){x}-16a^{2}+31a+9$ |
| 9.2-a2 |
9.2-a |
$2$ |
$3$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{8} \) |
$2.80291$ |
$(-a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$134.8680173$ |
1.378052898 |
\( \frac{5135}{9} a^{2} - \frac{1964}{9} a - \frac{25028}{9} \) |
\( \bigl[a\) , \( -a + 1\) , \( a^{2} + a - 3\) , \( a^{2} - 3 a - 4\) , \( -2 a - 1\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a^{2}-3a-4\right){x}-2a-1$ |
| 9.2-b1 |
9.2-b |
$2$ |
$5$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{8} \) |
$2.80291$ |
$(-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.2 |
$25$ |
\( 2 \) |
$1$ |
$0.531045949$ |
1.220875939 |
\( -\frac{44588942472159799443984364}{9} a^{2} - \frac{103894855095349922928862481}{9} a - \frac{19136402750270179594933979}{9} \) |
\( \bigl[a + 1\) , \( a^{2} + a - 3\) , \( a\) , \( -1441 a^{2} - 3372 a - 656\) , \( -75023 a^{2} - 174582 a - 31725\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(-1441a^{2}-3372a-656\right){x}-75023a^{2}-174582a-31725$ |
| 9.2-b2 |
9.2-b |
$2$ |
$5$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{16} \) |
$2.80291$ |
$(-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$13.27614874$ |
1.220875939 |
\( -\frac{712591111}{59049} a^{2} - \frac{1713781049}{59049} a - \frac{425773469}{59049} \) |
\( \bigl[a + 1\) , \( a^{2} + a - 3\) , \( a\) , \( -a^{2} - 2 a - 1\) , \( -9 a^{2} - 21 a - 5\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(-a^{2}-2a-1\right){x}-9a^{2}-21a-5$ |
| 11.1-a1 |
11.1-a |
$1$ |
$1$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$2.89824$ |
$(a^2-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$49.54874961$ |
2.278253934 |
\( -\frac{66252800}{11} a^{2} + \frac{141012992}{11} a + \frac{31129600}{11} \) |
\( \bigl[0\) , \( a + 1\) , \( a^{2} + a - 3\) , \( -a^{2} + a + 7\) , \( -4 a^{2} + 18\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a^{2}+a+7\right){x}-4a^{2}+18$ |
| 11.1-b1 |
11.1-b |
$1$ |
$1$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{2} \) |
$2.89824$ |
$(a^2-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.023019408$ |
$198.1252603$ |
1.258214530 |
\( -\frac{300364}{121} a^{2} + \frac{67319}{121} a + \frac{25769}{121} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - a - 2\) , \( 0\) , \( a^{2}\) , \( a^{2} - 3\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+a^{2}{x}+a^{2}-3$ |
| 15.1-a1 |
15.1-a |
$2$ |
$2$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{2} \cdot 5^{14} \) |
$3.05200$ |
$(-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$34.04036382$ |
1.565177596 |
\( -\frac{2393916574435937}{54931640625} a^{2} + \frac{448412068892543}{54931640625} a + \frac{11949963967855883}{54931640625} \) |
\( \bigl[a\) , \( -a^{2} + a + 2\) , \( a\) , \( 5 a^{2} - 2 a - 27\) , \( 15 a^{2} - 2 a - 72\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(5a^{2}-2a-27\right){x}+15a^{2}-2a-72$ |
| 15.1-a2 |
15.1-a |
$2$ |
$2$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3 \cdot 5^{7} \) |
$3.05200$ |
$(-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$136.1614553$ |
1.565177596 |
\( \frac{3891697856}{234375} a^{2} + \frac{9151847491}{234375} a + \frac{2095451821}{234375} \) |
\( \bigl[a\) , \( -a^{2} + a + 2\) , \( a\) , \( -2 a - 2\) , \( a - 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-2a-2\right){x}+a-1$ |
| 15.1-b1 |
15.1-b |
$8$ |
$12$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{12} \cdot 5^{12} \) |
$3.05200$ |
$(-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$3.852734021$ |
1.062893394 |
\( -\frac{2646439532869967303}{129746337890625} a^{2} - \frac{3787475185833111808}{129746337890625} a + \frac{15409961011960512902}{129746337890625} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} - 3\) , \( a + 1\) , \( 1065 a^{2} - 207 a - 5272\) , \( 28653 a^{2} - 5766 a - 142088\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(1065a^{2}-207a-5272\right){x}+28653a^{2}-5766a-142088$ |
| 15.1-b2 |
15.1-b |
$8$ |
$12$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{6} \cdot 5^{6} \) |
$3.05200$ |
$(-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$30.82187217$ |
1.062893394 |
\( \frac{3721513443770353}{11390625} a^{2} + \frac{8671344133377233}{11390625} a + \frac{1597196742142148}{11390625} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} - 3\) , \( a + 1\) , \( 115 a^{2} - 17 a - 557\) , \( -328 a^{2} + 75 a + 1645\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(115a^{2}-17a-557\right){x}-328a^{2}+75a+1645$ |
| 15.1-b3 |
15.1-b |
$8$ |
$12$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{3} \cdot 5^{3} \) |
$3.05200$ |
$(-a-1), (a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$123.2874886$ |
1.062893394 |
\( -\frac{472854046}{3375} a^{2} + \frac{140746669}{3375} a + \frac{2446736014}{3375} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} - 3\) , \( a + 1\) , \( 90 a^{2} - 12 a - 432\) , \( -746 a^{2} + 160 a + 3720\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(90a^{2}-12a-432\right){x}-746a^{2}+160a+3720$ |
| 15.1-b4 |
15.1-b |
$8$ |
$12$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{3} \cdot 5^{3} \) |
$3.05200$ |
$(-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 3 \) |
$1$ |
$7.705468043$ |
1.062893394 |
\( \frac{4066461370739367982921}{3375} a^{2} + \frac{9475093856005005299456}{3375} a + \frac{1745218393718466878486}{3375} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} - 3\) , \( a + 1\) , \( -435 a^{2} + 93 a + 2158\) , \( -1817 a^{2} + 356 a + 8998\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-435a^{2}+93a+2158\right){x}-1817a^{2}+356a+8998$ |
| 15.1-b5 |
15.1-b |
$8$ |
$12$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{4} \cdot 5^{4} \) |
$3.05200$ |
$(-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$11.55820206$ |
1.062893394 |
\( -\frac{19350650936528717828}{50625} a^{2} + \frac{3901858979508591167}{50625} a + \frac{95966485104145440752}{50625} \) |
\( \bigl[1\) , \( a^{2} + a - 2\) , \( a^{2} - 2\) , \( 432 a^{2} - 83 a - 2136\) , \( 7341 a^{2} - 1477 a - 36401\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(432a^{2}-83a-2136\right){x}+7341a^{2}-1477a-36401$ |
| 15.1-b6 |
15.1-b |
$8$ |
$12$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$3.05200$ |
$(-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$92.46561651$ |
1.062893394 |
\( \frac{26586189553}{225} a^{2} - \frac{60423986392}{225} a - \frac{3549058552}{225} \) |
\( \bigl[1\) , \( a^{2} + a - 2\) , \( a^{2} - 2\) , \( 27 a^{2} - 3 a - 131\) , \( 102 a^{2} - 20 a - 506\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(27a^{2}-3a-131\right){x}+102a^{2}-20a-506$ |
| 15.1-b7 |
15.1-b |
$8$ |
$12$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3 \cdot 5 \) |
$3.05200$ |
$(-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 1 \) |
$1$ |
$23.11640412$ |
1.062893394 |
\( \frac{2078760109429575484}{15} a^{2} - \frac{4424472646055366641}{15} a - \frac{976668619791817696}{15} \) |
\( \bigl[1\) , \( a^{2} + a - 2\) , \( a^{2} - 2\) , \( 22 a^{2} - 3 a - 126\) , \( 107 a^{2} - 47 a - 559\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(22a^{2}-3a-126\right){x}+107a^{2}-47a-559$ |
| 15.1-b8 |
15.1-b |
$8$ |
$12$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3 \cdot 5 \) |
$3.05200$ |
$(-a-1), (a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$369.8624660$ |
1.062893394 |
\( -\frac{15829}{15} a^{2} + \frac{271711}{15} a + \frac{165616}{15} \) |
\( \bigl[1\) , \( a^{2} + a - 2\) , \( a^{2} - 2\) , \( 2 a^{2} + 2 a - 6\) , \( a^{2} + a - 4\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(2a^{2}+2a-6\right){x}+a^{2}+a-4$ |
| 15.1-c1 |
15.1-c |
$2$ |
$2$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{5} \cdot 5 \) |
$3.05200$ |
$(-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 5 \) |
$0.072393534$ |
$159.6066409$ |
1.992284878 |
\( \frac{26360066}{1215} a^{2} + \frac{68663521}{1215} a + \frac{26498866}{1215} \) |
\( \bigl[a^{2} - 2\) , \( -a^{2} - a + 3\) , \( a + 1\) , \( -2 a^{2} + 6\) , \( a^{2} - 4 a + 1\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-2a^{2}+6\right){x}+a^{2}-4a+1$ |
| 15.1-c2 |
15.1-c |
$2$ |
$2$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{10} \cdot 5^{2} \) |
$3.05200$ |
$(-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.036196767$ |
$79.80332047$ |
1.992284878 |
\( -\frac{33497146703537}{1476225} a^{2} + \frac{6595884658193}{1476225} a + \frac{166492910518508}{1476225} \) |
\( \bigl[a^{2} - 2\) , \( -a^{2} - a + 3\) , \( a + 1\) , \( -17 a^{2} + 35 a + 6\) , \( 68 a^{2} - 146 a - 32\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-17a^{2}+35a+6\right){x}+68a^{2}-146a-32$ |
| 24.1-a1 |
24.1-a |
$1$ |
$1$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( - 2^{3} \cdot 3^{7} \) |
$3.30069$ |
$(-a-1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$31.89843030$ |
1.466691388 |
\( -\frac{19134709}{2187} a^{2} + \frac{82063181}{4374} a + \frac{18722051}{4374} \) |
\( \bigl[a + 1\) , \( a^{2} + a - 4\) , \( a\) , \( 2 a^{2} + 8 a + 7\) , \( -a^{2} - 3 a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(2a^{2}+8a+7\right){x}-a^{2}-3a-3$ |
| 24.1-b1 |
24.1-b |
$1$ |
$1$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( - 2^{12} \cdot 3^{2} \) |
$3.30069$ |
$(-a-1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.018052948$ |
$185.4908133$ |
1.847656445 |
\( -\frac{857899}{36} a^{2} + \frac{9748015}{144} a - \frac{3931163}{144} \) |
\( \bigl[a^{2} - 2\) , \( -a\) , \( a^{2} - 2\) , \( a^{2} + 3 a - 1\) , \( 2 a^{2} + 5 a\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}-a{x}^{2}+\left(a^{2}+3a-1\right){x}+2a^{2}+5a$ |
| 25.2-a1 |
25.2-a |
$2$ |
$3$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{8} \) |
$3.32322$ |
$(a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$44.42400219$ |
2.042617797 |
\( 23449 a^{2} - 50186 a - 11038 \) |
\( \bigl[a^{2} + a - 3\) , \( -a + 1\) , \( a^{2} + a - 3\) , \( -a^{2}\) , \( -a - 1\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a+1\right){x}^{2}-a^{2}{x}-a-1$ |
| 25.2-a2 |
25.2-a |
$2$ |
$3$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{8} \) |
$3.32322$ |
$(a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$14.80800073$ |
2.042617797 |
\( -180288704 a^{2} - 420092133 a - 77376998 \) |
\( \bigl[a^{2} - 2\) , \( 1\) , \( 0\) , \( -a^{2} + 7 a - 6\) , \( -22 a^{2} + 22 a + 70\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+{x}^{2}+\left(-a^{2}+7a-6\right){x}-22a^{2}+22a+70$ |
| 25.2-b1 |
25.2-b |
$2$ |
$5$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{9} \) |
$3.32322$ |
$(a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$14.87352350$ |
1.367770679 |
\( -2001865509 a^{2} - 4664476896 a - 859175027 \) |
\( \bigl[1\) , \( -a\) , \( a^{2} - 2\) , \( 236 a^{2} - 74 a - 1226\) , \( -3404 a^{2} + 595 a + 16686\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}-a{x}^{2}+\left(236a^{2}-74a-1226\right){x}-3404a^{2}+595a+16686$ |
| 25.2-b2 |
25.2-b |
$2$ |
$5$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{9} \) |
$3.32322$ |
$(a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$14.87352350$ |
1.367770679 |
\( -2556 a^{2} + 5451 a + 1243 \) |
\( \bigl[a + 1\) , \( -a^{2} - a + 2\) , \( a\) , \( -4 a^{2} + a + 19\) , \( 32 a^{2} - 7 a - 161\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-4a^{2}+a+19\right){x}+32a^{2}-7a-161$ |
| 25.2-c1 |
25.2-c |
$2$ |
$5$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{3} \) |
$3.32322$ |
$(a-1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$164.6085288$ |
0.605496657 |
\( -2556 a^{2} + 5451 a + 1243 \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( 0\) , \( a^{2} + a + 1\) , \( -4 a^{2} - 10 a - 2\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(a^{2}+a+1\right){x}-4a^{2}-10a-2$ |
| 25.2-c2 |
25.2-c |
$2$ |
$5$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{3} \) |
$3.32322$ |
$(a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$5$ |
5B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$6.584341153$ |
0.605496657 |
\( -2001865509 a^{2} - 4664476896 a - 859175027 \) |
\( \bigl[a + 1\) , \( a^{2} + a - 4\) , \( a^{2} + a - 2\) , \( -173 a^{2} - 401 a - 69\) , \( -3305 a^{2} - 7702 a - 1421\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-173a^{2}-401a-69\right){x}-3305a^{2}-7702a-1421$ |
| 25.2-d1 |
25.2-d |
$2$ |
$3$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{2} \) |
$3.32322$ |
$(a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.702143798$ |
$26.54291975$ |
2.570783140 |
\( -180288704 a^{2} - 420092133 a - 77376998 \) |
\( \bigl[a^{2} + a - 2\) , \( -a\) , \( a^{2} + a - 2\) , \( a^{2} - a - 8\) , \( 9 a^{2} - 2 a - 45\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}-a{x}^{2}+\left(a^{2}-a-8\right){x}+9a^{2}-2a-45$ |
| 25.2-d2 |
25.2-d |
$2$ |
$3$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{2} \) |
$3.32322$ |
$(a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.234047932$ |
$79.62875926$ |
2.570783140 |
\( 23449 a^{2} - 50186 a - 11038 \) |
\( \bigl[a\) , \( -a^{2} + 2\) , \( a\) , \( -3 a^{2} + 3 a + 2\) , \( -3 a^{2} + 3 a + 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-3a^{2}+3a+2\right){x}-3a^{2}+3a+1$ |
| 27.1-a1 |
27.1-a |
$2$ |
$3$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{17} \) |
$3.36612$ |
$(-a-1), (a^2-a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.206118124$ |
$67.16047973$ |
1.909504370 |
\( \frac{494468512378880}{14348907} a^{2} - \frac{99701437657088}{14348907} a - \frac{2452231729958912}{14348907} \) |
\( \bigl[0\) , \( a^{2} + a - 4\) , \( a^{2} - 2\) , \( -a^{2} + 3 a + 6\) , \( 178 a^{2} - 376 a - 86\bigr] \) |
${y}^2+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-a^{2}+3a+6\right){x}+178a^{2}-376a-86$ |
| 27.1-a2 |
27.1-a |
$2$ |
$3$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{11} \) |
$3.36612$ |
$(-a-1), (a^2-a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.068706041$ |
$201.4814391$ |
1.909504370 |
\( -\frac{404672512}{243} a^{2} + \frac{851660800}{243} a + \frac{188157952}{243} \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -770 a^{2} + 373 a + 107\) , \( 17961 a^{2} - 9847 a - 2716\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-770a^{2}+373a+107\right){x}+17961a^{2}-9847a-2716$ |
| 27.1-b1 |
27.1-b |
$1$ |
$1$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{7} \) |
$3.36612$ |
$(-a-1), (a^2-a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.055182854$ |
$94.53434721$ |
2.158766806 |
\( \frac{450560}{9} a^{2} - \frac{262144}{27} a - \frac{6713344}{27} \) |
\( \bigl[0\) , \( 1\) , \( a^{2} - 3\) , \( 6 a^{2} - a - 29\) , \( -10 a^{2} + 2 a + 49\bigr] \) |
${y}^2+\left(a^{2}-3\right){y}={x}^{3}+{x}^{2}+\left(6a^{2}-a-29\right){x}-10a^{2}+2a+49$ |
| 27.2-a1 |
27.2-a |
$1$ |
$1$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{11} \) |
$3.36612$ |
$(-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$35.97047619$ |
1.653924257 |
\( 26 a^{2} - 972 a - 2195 \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -a - 1\) , \( -a^{2} - 2 a\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-a-1\right){x}-a^{2}-2a$ |
| 27.2-b1 |
27.2-b |
$1$ |
$1$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{5} \) |
$3.36612$ |
$(-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$24.80640814$ |
1.140599861 |
\( 26 a^{2} - 972 a - 2195 \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} - a + 2\) , \( a\) , \( -a^{2} + 6\) , \( -a^{2} + 3\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-a^{2}+6\right){x}-a^{2}+3$ |
| 33.1-a1 |
33.1-a |
$4$ |
$4$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{5} \cdot 11 \) |
$3.48061$ |
$(-a-1), (-a^2-a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.417094904$ |
$134.2422927$ |
1.640057214 |
\( \frac{1060925}{2673} a^{2} - \frac{1433639}{2673} a - \frac{241352}{2673} \) |
\( \bigl[1\) , \( -a^{2} - a + 4\) , \( a^{2} + a - 2\) , \( -4 a^{2} + 6 a + 9\) , \( -6 a^{2} + 8 a + 4\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-4a^{2}+6a+9\right){x}-6a^{2}+8a+4$ |
| 33.1-a2 |
33.1-a |
$4$ |
$4$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( - 3^{20} \cdot 11^{4} \) |
$3.48061$ |
$(-a-1), (-a^2-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.417094904$ |
$8.390143296$ |
1.640057214 |
\( \frac{488022235510528}{421900912521} a^{2} + \frac{2301518454069641}{421900912521} a + \frac{2117964572279282}{421900912521} \) |
\( \bigl[1\) , \( -a^{2} - a + 4\) , \( a^{2} + a - 2\) , \( -34 a^{2} + 71 a + 19\) , \( -349 a^{2} + 742 a + 157\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-34a^{2}+71a+19\right){x}-349a^{2}+742a+157$ |
| 33.1-a3 |
33.1-a |
$4$ |
$4$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{10} \cdot 11^{2} \) |
$3.48061$ |
$(-a-1), (-a^2-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.708547452$ |
$67.12114637$ |
1.640057214 |
\( \frac{27330995881}{59049} a^{2} - \frac{643832868644}{649539} a - \frac{129857010260}{649539} \) |
\( \bigl[1\) , \( -a^{2} - a + 4\) , \( a^{2} + a - 2\) , \( -39 a^{2} + 81 a + 24\) , \( -288 a^{2} + 609 a + 135\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-39a^{2}+81a+24\right){x}-288a^{2}+609a+135$ |
| 33.1-a4 |
33.1-a |
$4$ |
$4$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{5} \cdot 11 \) |
$3.48061$ |
$(-a-1), (-a^2-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.417094904$ |
$33.56057318$ |
1.640057214 |
\( \frac{4992932946051328}{2673} a^{2} - \frac{10627389154786417}{2673} a - \frac{2345041704233458}{2673} \) |
\( \bigl[1\) , \( -a^{2} - a + 4\) , \( a^{2} + a - 2\) , \( -604 a^{2} + 1291 a + 269\) , \( -17255 a^{2} + 36720 a + 8117\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-604a^{2}+1291a+269\right){x}-17255a^{2}+36720a+8117$ |
| 33.2-a1 |
33.2-a |
$1$ |
$1$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( - 3 \cdot 11 \) |
$3.48061$ |
$(-a-1), (a^2-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$49.54270018$ |
2.277975781 |
\( \frac{2627917}{33} a^{2} - \frac{522745}{33} a - \frac{13049950}{33} \) |
\( \bigl[a^{2} - 2\) , \( -a^{2} + 4\) , \( 1\) , \( -1\) , \( 5 a^{2} - a - 25\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}-{x}+5a^{2}-a-25$ |
| 33.2-b1 |
33.2-b |
$1$ |
$1$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( - 3^{3} \cdot 11^{7} \) |
$3.48061$ |
$(-a-1), (a^2-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$1$ |
$12.71618945$ |
1.754073041 |
\( -\frac{1761876716816045}{526153617} a^{2} + \frac{3750080998104548}{526153617} a + \frac{827790522298475}{526153617} \) |
\( \bigl[a^{2} + a - 3\) , \( -a\) , \( a + 1\) , \( -5 a^{2} + 11 a + 6\) , \( -13 a^{2} + 39 a + 9\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-5a^{2}+11a+6\right){x}-13a^{2}+39a+9$ |
| 33.2-c1 |
33.2-c |
$2$ |
$3$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( - 3^{21} \cdot 11^{3} \) |
$3.48061$ |
$(-a-1), (a^2-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$11.85693286$ |
1.635547062 |
\( \frac{1726006026348265}{13922730113193} a^{2} - \frac{126345123968317}{13922730113193} a - \frac{7371402585728482}{13922730113193} \) |
\( \bigl[a^{2} + a - 3\) , \( -a + 1\) , \( a\) , \( 2 a^{2} + 4 a + 3\) , \( 17 a^{2} + 37 a + 4\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a^{2}+4a+3\right){x}+17a^{2}+37a+4$ |
| 33.2-c2 |
33.2-c |
$2$ |
$3$ |
3.3.473.1 |
$3$ |
$[3, 0]$ |
33.2 |
\( 3 \cdot 11 \) |
\( - 3^{7} \cdot 11 \) |
$3.48061$ |
$(-a-1), (a^2-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$35.57079860$ |
1.635547062 |
\( \frac{6654289418761}{24057} a^{2} - \frac{1337166702754}{24057} a - \frac{33037296917428}{24057} \) |
\( \bigl[a^{2} - 2\) , \( -a\) , \( a + 1\) , \( -6291 a^{2} - 14645 a - 2696\) , \( 643940 a^{2} + 1500403 a + 276359\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-6291a^{2}-14645a-2696\right){x}+643940a^{2}+1500403a+276359$ |
*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.
