| 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 |
| 64.1-b3 |
64.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \) |
$1.33740$ |
$(a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$1.494440753$ |
$13.75037163$ |
1.941708926 |
\( 287496 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 134 a - 345\) , \( 1298 a - 3425\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(134a-345\right){x}+1298a-3425$ |
| 64.1-b4 |
64.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \) |
$1.33740$ |
$(a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$1.494440753$ |
$55.00148654$ |
1.941708926 |
\( 287496 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 135 a - 341\) , \( -1379 a + 3661\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(135a-341\right){x}-1379a+3661$ |
| 256.1-g3 |
256.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{18} \) |
$1.89137$ |
$(a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.067060424$ |
$6.875185818$ |
2.772837593 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 528 a - 1397\) , \( 10710 a - 28336\bigr] \) |
${y}^2={x}^{3}+\left(528a-1397\right){x}+10710a-28336$ |
| 256.1-g4 |
256.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{18} \) |
$1.89137$ |
$(a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.067060424$ |
$27.50074327$ |
2.772837593 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 528 a - 1397\) , \( -10710 a + 28336\bigr] \) |
${y}^2={x}^{3}+\left(528a-1397\right){x}-10710a+28336$ |
| 576.2-a3 |
576.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
576.2 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{6} \) |
$2.31645$ |
$(a+3), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$15.87756153$ |
1.500288544 |
\( 287496 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 14 a - 22\) , \( -35 a + 102\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(14a-22\right){x}-35a+102$ |
| 576.2-a4 |
576.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
576.2 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{6} \) |
$2.31645$ |
$(a+3), (-a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$15.87756153$ |
1.500288544 |
\( 287496 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 13 a - 26\) , \( 31 a - 75\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(13a-26\right){x}+31a-75$ |
| 576.3-a3 |
576.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{6} \) |
$2.31645$ |
$(a+3), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$15.87756153$ |
1.500288544 |
\( 287496 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -8 a - 22\) , \( -57 a - 150\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-8a-22\right){x}-57a-150$ |
| 576.3-a4 |
576.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
576.3 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{6} \) |
$2.31645$ |
$(a+3), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$15.87756153$ |
1.500288544 |
\( 287496 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -9 a - 26\) , \( 9 a + 23\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-9a-26\right){x}+9a+23$ |
*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.
