| 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 |
| 31.1-a4 |
31.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{8} \) |
$0.47148$ |
$(5a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1.609651241$ |
0.359928959 |
\( \frac{11889611722383394}{852891037441} a - \frac{8629385062119691}{852891037441} \) |
\( \bigl[1\) , \( \phi + 1\) , \( \phi\) , \( 31 \phi - 75\) , \( 141 \phi - 303\bigr] \) |
${y}^2+{x}{y}+\phi{y}={x}^{3}+\left(\phi+1\right){x}^{2}+\left(31\phi-75\right){x}+141\phi-303$ |
| 775.1-a4 |
775.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
775.1 |
\( 5^{2} \cdot 31 \) |
\( - 5^{6} \cdot 31^{8} \) |
$1.05426$ |
$(-2a+1), (5a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.373228461$ |
1.508553628 |
\( \frac{11889611722383394}{852891037441} a - \frac{8629385062119691}{852891037441} \) |
\( \bigl[\phi + 1\) , \( \phi - 1\) , \( 1\) , \( -76 \phi - 227\) , \( 447 \phi + 1348\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(-76\phi-227\right){x}+447\phi+1348$ |
| 961.2-c4 |
961.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
961.2 |
\( 31^{2} \) |
\( - 31^{14} \) |
$1.11251$ |
$(5a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.548353402$ |
$0.430920289$ |
1.367630581 |
\( \frac{11889611722383394}{852891037441} a - \frac{8629385062119691}{852891037441} \) |
\( \bigl[\phi + 1\) , \( -\phi\) , \( 0\) , \( 652 \phi - 2048\) , \( 27054 \phi - 32629\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}-\phi{x}^{2}+\left(652\phi-2048\right){x}+27054\phi-32629$ |
| 2511.1-f4 |
2511.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2511.1 |
\( 3^{4} \cdot 31 \) |
\( - 3^{12} \cdot 31^{8} \) |
$1.41444$ |
$(5a-2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.514256047$ |
1.124409487 |
\( \frac{11889611722383394}{852891037441} a - \frac{8629385062119691}{852891037441} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 273 \phi - 683\) , \( -3940 \phi + 7771\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(273\phi-683\right){x}-3940\phi+7771$ |
| 3751.4-b4 |
3751.4-b |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3751.4 |
\( 11^{2} \cdot 31 \) |
\( - 11^{6} \cdot 31^{8} \) |
$1.56372$ |
$(-3a+2), (5a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.525767693$ |
2.729376224 |
\( \frac{11889611722383394}{852891037441} a - \frac{8629385062119691}{852891037441} \) |
\( \bigl[\phi + 1\) , \( \phi\) , \( \phi + 1\) , \( 531 \phi - 1077\) , \( -10221 \phi + 15145\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}+\left(\phi+1\right){y}={x}^{3}+\phi{x}^{2}+\left(531\phi-1077\right){x}-10221\phi+15145$ |
| 3751.6-a4 |
3751.6-a |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3751.6 |
\( 11^{2} \cdot 31 \) |
\( - 11^{6} \cdot 31^{8} \) |
$1.56372$ |
$(-3a+1), (5a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.723404901$ |
2.588132054 |
\( \frac{11889611722383394}{852891037441} a - \frac{8629385062119691}{852891037441} \) |
\( \bigl[\phi\) , \( 1\) , \( 0\) , \( 167 \phi - 667\) , \( 5143 \phi - 5708\bigr] \) |
${y}^2+\phi{x}{y}={x}^{3}+{x}^{2}+\left(167\phi-667\right){x}+5143\phi-5708$ |
*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.
