| 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 |
$4$ |
$14$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.66870$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.874073183 |
\( -3375 \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 2 a + 10\) , \( 2 a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(2a+10\right){x}+2a+7$ |
| 1.1-a2 |
1.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.66870$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.874073183 |
\( -3375 \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 4 a + 3\) , \( a + 21\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(4a+3\right){x}+a+21$ |
| 1.1-a3 |
1.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.66870$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.874073183 |
\( 16581375 \) |
\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -18 a - 65\) , \( 41 a + 153\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-18a-65\right){x}+41a+153$ |
| 1.1-a4 |
1.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.66870$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.874073183 |
\( 16581375 \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 24 a - 72\) , \( -113 a + 447\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(24a-72\right){x}-113a+447$ |
| 5.1-a1 |
5.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{9} \) |
$0.99994$ |
$(-a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 1 \) |
$1$ |
$11.70663218$ |
1.564364528 |
\( \frac{534684321}{1953125} a + \frac{3601913643}{1953125} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -15 a - 54\) , \( -33 a - 127\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-15a-54\right){x}-33a-127$ |
| 5.1-b1 |
5.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( - 5^{9} \) |
$0.99994$ |
$(-a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 3^{2} \) |
$0.053182667$ |
$11.35679518$ |
1.452795207 |
\( \frac{534684321}{1953125} a + \frac{3601913643}{1953125} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -8 a + 30\) , \( 27 a - 101\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-8a+30\right){x}+27a-101$ |
| 5.2-a1 |
5.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{9} \) |
$0.99994$ |
$(-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 1 \) |
$1$ |
$11.70663218$ |
1.564364528 |
\( -\frac{534684321}{1953125} a + \frac{3601913643}{1953125} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( 14 a - 54\) , \( 33 a - 127\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(14a-54\right){x}+33a-127$ |
| 5.2-b1 |
5.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
5.2 |
\( 5 \) |
\( - 5^{9} \) |
$0.99994$ |
$(-a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Nn |
$1$ |
\( 3^{2} \) |
$0.053182667$ |
$11.35679518$ |
1.452795207 |
\( -\frac{534684321}{1953125} a + \frac{3601913643}{1953125} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 8 a + 30\) , \( -27 a - 101\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(8a+30\right){x}-27a-101$ |
| 10.1-a1 |
10.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5 \) |
$1.18914$ |
$(-a+4), (-a+3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$36.43104508$ |
1.081845150 |
\( \frac{5689}{20} a + \frac{21627}{20} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2 a + 7\) , \( -30 a + 112\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-2a+7\right){x}-30a+112$ |
| 10.1-a2 |
10.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{12} \cdot 5^{3} \) |
$1.18914$ |
$(-a+4), (-a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$4.047893897$ |
1.081845150 |
\( \frac{18258829169}{8000} a + \frac{68318145777}{8000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 18 a - 68\) , \( 814 a - 3046\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(18a-68\right){x}+814a-3046$ |
| 10.1-b1 |
10.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{10} \cdot 5^{5} \) |
$1.18914$ |
$(-a+4), (-a+3)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \cdot 5^{2} \) |
$1$ |
$8.284026412$ |
2.213999186 |
\( \frac{73603923}{100000} a + \frac{358833109}{100000} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -27 a - 102\) , \( -216 a - 811\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-27a-102\right){x}-216a-811$ |
| 10.1-b2 |
10.1-b |
$2$ |
$5$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5 \) |
$1.18914$ |
$(-a+4), (-a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 2 \) |
$1$ |
$0.331361056$ |
2.213999186 |
\( \frac{7114676554418062503}{10} a + \frac{26620682081199569989}{10} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -17217 a - 64432\) , \( -2427316 a - 9082191\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-17217a-64432\right){x}-2427316a-9082191$ |
| 10.1-c1 |
10.1-c |
$2$ |
$5$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{10} \cdot 5^{5} \) |
$1.18914$ |
$(-a+4), (-a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$0.054400494$ |
$14.16313473$ |
2.059198521 |
\( \frac{73603923}{100000} a + \frac{358833109}{100000} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -5 a + 29\) , \( -20 a + 81\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-5a+29\right){x}-20a+81$ |
| 10.1-c2 |
10.1-c |
$2$ |
$5$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5 \) |
$1.18914$ |
$(-a+4), (-a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$0.272002473$ |
$14.16313473$ |
2.059198521 |
\( \frac{7114676554418062503}{10} a + \frac{26620682081199569989}{10} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 1285 a - 4941\) , \( -48650 a + 182431\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(1285a-4941\right){x}-48650a+182431$ |
| 10.1-d1 |
10.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5 \) |
$1.18914$ |
$(-a+4), (-a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.115049867$ |
$20.19548844$ |
1.241956719 |
\( \frac{5689}{20} a + \frac{21627}{20} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 3\) , \( 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+3{x}+1$ |
| 10.1-d2 |
10.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{12} \cdot 5^{3} \) |
$1.18914$ |
$(-a+4), (-a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.038349955$ |
$20.19548844$ |
1.241956719 |
\( \frac{18258829169}{8000} a + \frac{68318145777}{8000} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -20 a - 72\) , \( 128 a + 480\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-20a-72\right){x}+128a+480$ |
| 10.2-a1 |
10.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{12} \cdot 5^{3} \) |
$1.18914$ |
$(-a+4), (-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$4.047893897$ |
1.081845150 |
\( -\frac{18258829169}{8000} a + \frac{68318145777}{8000} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -18 a - 68\) , \( -814 a - 3046\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-18a-68\right){x}-814a-3046$ |
| 10.2-a2 |
10.2-a |
$2$ |
$3$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5 \) |
$1.18914$ |
$(-a+4), (-a-3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$36.43104508$ |
1.081845150 |
\( -\frac{5689}{20} a + \frac{21627}{20} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 2 a + 7\) , \( 30 a + 112\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(2a+7\right){x}+30a+112$ |
| 10.2-b1 |
10.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5 \) |
$1.18914$ |
$(-a+4), (-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 2 \) |
$1$ |
$0.331361056$ |
2.213999186 |
\( -\frac{7114676554418062503}{10} a + \frac{26620682081199569989}{10} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 17221 a - 64425\) , \( 2362884 a - 8841125\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(17221a-64425\right){x}+2362884a-8841125$ |
| 10.2-b2 |
10.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{10} \cdot 5^{5} \) |
$1.18914$ |
$(-a+4), (-a-3)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2 \cdot 5^{2} \) |
$1$ |
$8.284026412$ |
2.213999186 |
\( -\frac{73603923}{100000} a + \frac{358833109}{100000} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 31 a - 95\) , \( 114 a - 405\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(31a-95\right){x}+114a-405$ |
| 10.2-c1 |
10.2-c |
$2$ |
$5$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{2} \cdot 5 \) |
$1.18914$ |
$(-a+4), (-a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$0.272002473$ |
$14.16313473$ |
2.059198521 |
\( -\frac{7114676554418062503}{10} a + \frac{26620682081199569989}{10} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -1285 a - 4941\) , \( 48650 a + 182431\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-1285a-4941\right){x}+48650a+182431$ |
| 10.2-c2 |
10.2-c |
$2$ |
$5$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{10} \cdot 5^{5} \) |
$1.18914$ |
$(-a+4), (-a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$0.054400494$ |
$14.16313473$ |
2.059198521 |
\( -\frac{73603923}{100000} a + \frac{358833109}{100000} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 5 a + 29\) , \( 20 a + 81\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(5a+29\right){x}+20a+81$ |
| 10.2-d1 |
10.2-d |
$2$ |
$3$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{12} \cdot 5^{3} \) |
$1.18914$ |
$(-a+4), (-a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.038349955$ |
$20.19548844$ |
1.241956719 |
\( -\frac{18258829169}{8000} a + \frac{68318145777}{8000} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 20 a - 72\) , \( -128 a + 480\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(20a-72\right){x}-128a+480$ |
| 10.2-d2 |
10.2-d |
$2$ |
$3$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2^{4} \cdot 5 \) |
$1.18914$ |
$(-a+4), (-a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.115049867$ |
$20.19548844$ |
1.241956719 |
\( -\frac{5689}{20} a + \frac{21627}{20} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 3\) , \( 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+3{x}+1$ |
| 14.1-a1 |
14.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{36} \cdot 7^{2} \) |
$1.29349$ |
$(-a+4), (-2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$12.63051067$ |
$0.436190660$ |
1.472425245 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$ |
| 14.1-a2 |
14.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$1.29349$ |
$(-a+4), (-2a+7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1.403390075$ |
$35.33144352$ |
1.472425245 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}$ |
| 14.1-a3 |
14.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \) |
$1.29349$ |
$(-a+4), (-2a+7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$4.210170225$ |
$3.925715946$ |
1.472425245 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$ |
| 14.1-a4 |
14.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{6} \cdot 7^{12} \) |
$1.29349$ |
$(-a+4), (-2a+7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$2.105085112$ |
$3.925715946$ |
1.472425245 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$ |
| 14.1-a5 |
14.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{2} \cdot 7^{4} \) |
$1.29349$ |
$(-a+4), (-2a+7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \) |
$0.701695037$ |
$35.33144352$ |
1.472425245 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$ |
| 14.1-a6 |
14.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{18} \cdot 7^{4} \) |
$1.29349$ |
$(-a+4), (-2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$6.315255337$ |
$0.436190660$ |
1.472425245 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$ |
| 14.1-b1 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{36} \cdot 7^{2} \) |
$1.29349$ |
$(-a+4), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.027708105$ |
0.939116998 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 20462 a - 76559\) , \( -3121544 a + 11679749\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(20462a-76559\right){x}-3121544a+11679749$ |
| 14.1-b2 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$1.29349$ |
$(-a+4), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.027708105$ |
0.939116998 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 62 a - 229\) , \( 960 a - 3591\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(62a-229\right){x}+960a-3591$ |
| 14.1-b3 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{12} \cdot 7^{6} \) |
$1.29349$ |
$(-a+4), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$7.027708105$ |
0.939116998 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -538 a + 2016\) , \( -21216 a + 79384\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-538a+2016\right){x}-21216a+79384$ |
| 14.1-b4 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{6} \cdot 7^{12} \) |
$1.29349$ |
$(-a+4), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$7.027708105$ |
0.939116998 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 4262 a - 15944\) , \( -246560 a + 922544\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4262a-15944\right){x}-246560a+922544$ |
| 14.1-b5 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{2} \cdot 7^{4} \) |
$1.29349$ |
$(-a+4), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.027708105$ |
0.939116998 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 1262 a - 4719\) , \( 45312 a - 169541\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1262a-4719\right){x}+45312a-169541$ |
| 14.1-b6 |
14.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
14.1 |
\( 2 \cdot 7 \) |
\( 2^{18} \cdot 7^{4} \) |
$1.29349$ |
$(-a+4), (-2a+7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.027708105$ |
0.939116998 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 327662 a - 1225999\) , \( -197976456 a + 740760069\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(327662a-1225999\right){x}-197976456a+740760069$ |
| 16.1-a1 |
16.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$1.33740$ |
$(-a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$13.08192952$ |
1.748146366 |
\( -3375 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -5 a - 19\) , \( 7 a + 26\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-5a-19\right){x}+7a+26$ |
| 16.1-a2 |
16.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$1.33740$ |
$(-a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$13.08192952$ |
1.748146366 |
\( -3375 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 5 a - 19\) , \( -7 a + 26\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(5a-19\right){x}-7a+26$ |
| 16.1-a3 |
16.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$1.33740$ |
$(-a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$13.08192952$ |
1.748146366 |
\( 16581375 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -85 a - 319\) , \( 699 a + 2614\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-85a-319\right){x}+699a+2614$ |
| 16.1-a4 |
16.1-a |
$4$ |
$14$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$1.33740$ |
$(-a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$13.08192952$ |
1.748146366 |
\( 16581375 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 85 a - 319\) , \( -699 a + 2614\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(85a-319\right){x}-699a+2614$ |
| 18.1-a1 |
18.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$1.37737$ |
$(-a+4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.501880177$ |
1.136111527 |
\( \frac{4913}{1296} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 2\) , \( -38 a - 142\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+2{x}-38a-142$ |
| 18.1-a2 |
18.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{16} \) |
$1.37737$ |
$(-a+4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.501880177$ |
1.136111527 |
\( \frac{838561807}{26244} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -80 a - 298\) , \( -738 a - 2762\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-80a-298\right){x}-738a-2762$ |
| 18.1-b1 |
18.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$1.37737$ |
$(-a+4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.501880177$ |
1.136111527 |
\( \frac{4913}{1296} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -a + 2\) , \( 38 a - 142\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-a+2\right){x}+38a-142$ |
| 18.1-b2 |
18.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
18.1 |
\( 2 \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{16} \) |
$1.37737$ |
$(-a+4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.501880177$ |
1.136111527 |
\( \frac{838561807}{26244} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 79 a - 298\) , \( 738 a - 2762\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(79a-298\right){x}+738a-2762$ |
| 20.1-a1 |
20.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{8} \cdot 5 \) |
$1.41413$ |
$(-a+4), (-a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$13.92592824$ |
1.860930439 |
\( \frac{3236}{5} a + \frac{12108}{5} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -13 a - 26\) , \( -32 a - 99\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-13a-26\right){x}-32a-99$ |
| 20.1-b1 |
20.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
20.1 |
\( 2^{2} \cdot 5 \) |
\( - 2^{8} \cdot 5 \) |
$1.41413$ |
$(-a+4), (-a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$0.223019342$ |
$31.97666518$ |
1.905950784 |
\( \frac{3236}{5} a + \frac{12108}{5} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 2\) , \( -2 a + 8\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+2{x}-2a+8$ |
| 20.2-a1 |
20.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( - 2^{8} \cdot 5 \) |
$1.41413$ |
$(-a+4), (-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$13.92592824$ |
1.860930439 |
\( -\frac{3236}{5} a + \frac{12108}{5} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 13 a - 26\) , \( 32 a - 99\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(13a-26\right){x}+32a-99$ |
| 20.2-b1 |
20.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
20.2 |
\( 2^{2} \cdot 5 \) |
\( - 2^{8} \cdot 5 \) |
$1.41413$ |
$(-a+4), (-a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$0.223019342$ |
$31.97666518$ |
1.905950784 |
\( -\frac{3236}{5} a + \frac{12108}{5} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 2\) , \( 2 a + 8\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+2{x}+2a+8$ |
| 22.1-a1 |
22.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{4} \cdot 11^{2} \) |
$1.44823$ |
$(-a+4), (a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.350694013$ |
$18.00713737$ |
1.687753482 |
\( \frac{69372345}{242} a - \frac{519137881}{484} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -28 a - 98\) , \( -2405 a - 8994\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-28a-98\right){x}-2405a-8994$ |
| 22.1-a2 |
22.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
22.1 |
\( 2 \cdot 11 \) |
\( 2^{2} \cdot 11 \) |
$1.44823$ |
$(-a+4), (a-5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.701388027$ |
$18.00713737$ |
1.687753482 |
\( -\frac{13538239447075}{22} a + \frac{50655455887741}{22} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -1538 a - 5748\) , \( -63797 a - 238702\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-1538a-5748\right){x}-63797a-238702$ |
*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.
