| 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-a2 |
31.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{2} \) |
$0.47148$ |
$(5a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1.609651241$ |
0.359928959 |
\( -\frac{61725871986044215714}{961} a + \frac{99874558858644938523}{961} \) |
\( \bigl[\phi\) , \( -1\) , \( \phi + 1\) , \( 133 \phi - 141\) , \( 737 \phi - 764\bigr] \) |
${y}^2+\phi{x}{y}+\left(\phi+1\right){y}={x}^{3}-{x}^{2}+\left(133\phi-141\right){x}+737\phi-764$ |
| 775.1-a2 |
775.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
775.1 |
\( 5^{2} \cdot 31 \) |
\( - 5^{6} \cdot 31^{2} \) |
$1.05426$ |
$(-2a+1), (5a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.373228461$ |
1.508553628 |
\( -\frac{61725871986044215714}{961} a + \frac{99874558858644938523}{961} \) |
\( \bigl[1\) , \( 1\) , \( \phi + 1\) , \( 637 \phi - 33\) , \( -10552 \phi - 3303\bigr] \) |
${y}^2+{x}{y}+\left(\phi+1\right){y}={x}^{3}+{x}^{2}+\left(637\phi-33\right){x}-10552\phi-3303$ |
| 961.2-c2 |
961.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
961.2 |
\( 31^{2} \) |
\( - 31^{8} \) |
$1.11251$ |
$(5a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$14.19341360$ |
$0.215460144$ |
1.367630581 |
\( -\frac{61725871986044215714}{961} a + \frac{99874558858644938523}{961} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 3856 \phi - 3410\) , \( 31874 \phi - 150499\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(3856\phi-3410\right){x}+31874\phi-150499$ |
| 2511.1-f2 |
2511.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
2511.1 |
\( 3^{4} \cdot 31 \) |
\( - 3^{12} \cdot 31^{2} \) |
$1.41444$ |
$(5a-2), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.514256047$ |
1.124409487 |
\( -\frac{61725871986044215714}{961} a + \frac{99874558858644938523}{961} \) |
\( \bigl[\phi\) , \( -\phi - 1\) , \( 1\) , \( 1207 \phi - 1266\) , \( -21126 \phi + 21880\bigr] \) |
${y}^2+\phi{x}{y}+{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(1207\phi-1266\right){x}-21126\phi+21880$ |
| 3751.4-b2 |
3751.4-b |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3751.4 |
\( 11^{2} \cdot 31 \) |
\( - 11^{6} \cdot 31^{2} \) |
$1.56372$ |
$(-3a+2), (5a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.051535386$ |
2.729376224 |
\( -\frac{61725871986044215714}{961} a + \frac{99874558858644938523}{961} \) |
\( \bigl[1\) , \( \phi - 1\) , \( 0\) , \( 1763 \phi - 2231\) , \( -28979 \phi + 57275\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(\phi-1\right){x}^{2}+\left(1763\phi-2231\right){x}-28979\phi+57275$ |
| 3751.6-a2 |
3751.6-a |
$6$ |
$8$ |
\(\Q(\sqrt{5}) \) |
$2$ |
$[2, 0]$ |
3751.6 |
\( 11^{2} \cdot 31 \) |
\( - 11^{6} \cdot 31^{2} \) |
$1.56372$ |
$(-3a+1), (5a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.361702450$ |
2.588132054 |
\( -\frac{61725871986044215714}{961} a + \frac{99874558858644938523}{961} \) |
\( \bigl[\phi + 1\) , \( \phi + 1\) , \( 0\) , \( 1324 \phi - 1003\) , \( 2987 \phi - 28326\bigr] \) |
${y}^2+\left(\phi+1\right){x}{y}={x}^{3}+\left(\phi+1\right){x}^{2}+\left(1324\phi-1003\right){x}+2987\phi-28326$ |
*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.
