| 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 |
| 2.1-a1 |
2.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{8} \) |
$2.02743$ |
$(2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$25.01220542$ |
2.621991567 |
\( -\frac{155788139}{16} a - \frac{743048891}{8} \) |
\( \bigl[1\) , \( -a\) , \( 0\) , \( -1061597 a - 10126958\) , \( 1842215936 a + 17573620023\bigr] \) |
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-1061597a-10126958\right){x}+1842215936a+17573620023$ |
| 2.1-b1 |
2.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{20} \) |
$2.02743$ |
$(2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$4.372706837$ |
0.458384227 |
\( \frac{155788139}{16} a - \frac{743048891}{8} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 9 a + 152\) , \( 51 a + 634\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(9a+152\right){x}+51a+634$ |
| 2.1-c1 |
2.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{8} \) |
$2.02743$ |
$(2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.992285400$ |
$4.372706837$ |
3.638783813 |
\( \frac{155788139}{16} a - \frac{743048891}{8} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 1061581 a - 10126770\) , \( 1850708648 a - 17654635191\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1061581a-10126770\right){x}+1850708648a-17654635191$ |
| 2.1-d1 |
2.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{8} \) |
$2.02743$ |
$(2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.992285400$ |
$4.372706837$ |
3.638783813 |
\( -\frac{155788139}{16} a - \frac{743048891}{8} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -1061581 a - 10126770\) , \( -1850708648 a - 17654635191\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1061581a-10126770\right){x}-1850708648a-17654635191$ |
| 2.1-e1 |
2.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{20} \) |
$2.02743$ |
$(2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.256357411$ |
$25.01220542$ |
5.377335760 |
\( -\frac{155788139}{16} a - \frac{743048891}{8} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 5 a + 183\) , \( 14 a + 513\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(5a+183\right){x}+14a+513$ |
| 2.1-f1 |
2.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{20} \) |
$2.02743$ |
$(2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{3} \) |
$0.256357411$ |
$25.01220542$ |
5.377335760 |
\( \frac{155788139}{16} a - \frac{743048891}{8} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -5 a + 183\) , \( -14 a + 513\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a+183\right){x}-14a+513$ |
| 2.1-g1 |
2.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{8} \) |
$2.02743$ |
$(2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$25.01220542$ |
2.621991567 |
\( \frac{155788139}{16} a - \frac{743048891}{8} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( 1061597 a - 10126958\) , \( -1842215936 a + 17573620023\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(1061597a-10126958\right){x}-1842215936a+17573620023$ |
| 2.1-h1 |
2.1-h |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
2.1 |
\( 2 \) |
\( 2^{20} \) |
$2.02743$ |
$(2,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$4.372706837$ |
0.458384227 |
\( -\frac{155788139}{16} a - \frac{743048891}{8} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -11 a + 152\) , \( -52 a + 634\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-11a+152\right){x}-52a+634$ |
| 4.1-a1 |
4.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$2.41104$ |
$(2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.885641966$ |
$34.68464615$ |
3.220140045 |
\( -1024 a - 8192 \) |
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( -2095 a - 19948\) , \( 162751 a + 1552484\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2095a-19948\right){x}+162751a+1552484$ |
| 4.1-b1 |
4.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{16} \) |
$2.41104$ |
$(2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$3.769655056$ |
$11.99765125$ |
4.741078534 |
\( 1024 a - 8192 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 18 a + 196\) , \( 102 a + 950\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(18a+196\right){x}+102a+950$ |
| 4.1-c1 |
4.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$2.41104$ |
$(2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$1.410417725$ |
$11.99765125$ |
5.321628452 |
\( -1024 a - 8192 \) |
\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -2095 a - 19948\) , \( -162752 a - 1552530\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2095a-19948\right){x}-162752a-1552530$ |
| 4.1-d1 |
4.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$2.41104$ |
$(2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$1.410417725$ |
$11.99765125$ |
5.321628452 |
\( 1024 a - 8192 \) |
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( 2095 a - 19948\) , \( 162751 a - 1552530\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2095a-19948\right){x}+162751a-1552530$ |
| 4.1-e1 |
4.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{16} \) |
$2.41104$ |
$(2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.129610578$ |
$34.68464615$ |
1.413768412 |
\( 1024 a - 8192 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 18 a + 196\) , \( -102 a - 950\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(18a+196\right){x}-102a-950$ |
| 4.1-f1 |
4.1-f |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{16} \) |
$2.41104$ |
$(2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.129610578$ |
$34.68464615$ |
1.413768412 |
\( -1024 a - 8192 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -18 a + 196\) , \( 102 a - 950\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-18a+196\right){x}+102a-950$ |
| 4.1-g1 |
4.1-g |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$2.41104$ |
$(2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.885641966$ |
$34.68464615$ |
3.220140045 |
\( 1024 a - 8192 \) |
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( 2095 a - 19948\) , \( -162752 a + 1552484\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2095a-19948\right){x}-162752a+1552484$ |
| 4.1-h1 |
4.1-h |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{16} \) |
$2.41104$ |
$(2,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$3.769655056$ |
$11.99765125$ |
4.741078534 |
\( -1024 a - 8192 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -18 a + 196\) , \( -102 a + 950\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-18a+196\right){x}-102a+950$ |
| 5.1-a1 |
5.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( 2^{12} \cdot 5^{2} \) |
$2.54936$ |
$(5,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.045674861$ |
$26.95063503$ |
0.258080708 |
\( -\frac{2471}{25} a - \frac{21334}{25} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -1297 a - 12152\) , \( 101038 a + 964616\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-1297a-12152\right){x}+101038a+964616$ |
| 5.1-b1 |
5.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$2.54936$ |
$(5,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$16.23396400$ |
1.701781830 |
\( -\frac{2471}{25} a - \frac{21334}{25} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( -21 a + 213\) , \( -225 a + 2209\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-21a+213\right){x}-225a+2209$ |
| 5.1-c1 |
5.1-c |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( 5^{2} \) |
$2.54936$ |
$(5,a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$26.95063503$ |
2.825194204 |
\( -\frac{2471}{25} a - \frac{21334}{25} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -5 a + 86\) , \( 121 a - 1108\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5a+86\right){x}+121a-1108$ |
| 5.1-d1 |
5.1-d |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
5.1 |
\( 5 \) |
\( 2^{12} \cdot 5^{2} \) |
$2.54936$ |
$(5,a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1.764120020$ |
$16.23396400$ |
6.004294795 |
\( -\frac{2471}{25} a - \frac{21334}{25} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -1281 a - 12121\) , \( -120366 a - 1148029\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-1281a-12121\right){x}-120366a-1148029$ |
| 5.2-a1 |
5.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
5.2 |
\( 5 \) |
\( 2^{12} \cdot 5^{2} \) |
$2.54936$ |
$(5,a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.045674861$ |
$26.95063503$ |
0.258080708 |
\( \frac{2471}{25} a - \frac{21334}{25} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 1295 a - 12152\) , \( -101039 a + 964616\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(1295a-12152\right){x}-101039a+964616$ |
| 5.2-b1 |
5.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
5.2 |
\( 5 \) |
\( 5^{2} \) |
$2.54936$ |
$(5,a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$16.23396400$ |
1.701781830 |
\( \frac{2471}{25} a - \frac{21334}{25} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( 21 a + 213\) , \( 225 a + 2209\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(21a+213\right){x}+225a+2209$ |
| 5.2-c1 |
5.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
5.2 |
\( 5 \) |
\( 5^{2} \) |
$2.54936$ |
$(5,a+4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$26.95063503$ |
2.825194204 |
\( \frac{2471}{25} a - \frac{21334}{25} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 5 a + 86\) , \( -121 a - 1108\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(5a+86\right){x}-121a-1108$ |
| 5.2-d1 |
5.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{91}) \) |
$2$ |
$[2, 0]$ |
5.2 |
\( 5 \) |
\( 2^{12} \cdot 5^{2} \) |
$2.54936$ |
$(5,a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1.764120020$ |
$16.23396400$ |
6.004294795 |
\( \frac{2471}{25} a - \frac{21334}{25} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 1281 a - 12121\) , \( 120366 a - 1148029\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1281a-12121\right){x}+120366a-1148029$ |
*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.
