| 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 |
| 32.1-a1 |
32.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$2.88294$ |
$(-23a+156)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$27.50074327$ |
1.013690845 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3588 a - 24335\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-3588a-24335\right){x}$ |
| 32.1-a2 |
32.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$2.88294$ |
$(-23a+156)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$13.75037163$ |
1.013690845 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3588 a + 24335\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-3588a+24335\right){x}$ |
| 32.1-b1 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$2.88294$ |
$(-23a+156)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$4.530611870$ |
$27.50074327$ |
2.296319889 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}$ |
| 32.1-b2 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$2.88294$ |
$(-23a+156)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$9.061223740$ |
$13.75037163$ |
2.296319889 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 174627960 a + 1184384449\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(174627960a+1184384449\right){x}$ |
| 32.1-b3 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$2.88294$ |
$(-23a+156)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$2.265305935$ |
$13.75037163$ |
2.296319889 |
\( 287496 \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -480226890 a - 3257057198\) , \( -14875180710936 a - 100888384140145\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-480226890a-3257057198\right){x}-14875180710936a-100888384140145$ |
| 32.1-b4 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$2.88294$ |
$(-23a+156)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$2.265305935$ |
$55.00148654$ |
2.296319889 |
\( 287496 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -480226890 a - 3257057221\) , \( 14871819122706 a + 100865584739576\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-480226890a-3257057221\right){x}+14871819122706a+100865584739576$ |
| 32.1-c1 |
32.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$2.88294$ |
$(-23a+156)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$5.183939605$ |
$13.75037163$ |
5.254912124 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}$ |
| 32.1-c2 |
32.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$2.88294$ |
$(-23a+156)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$10.36787921$ |
$27.50074327$ |
5.254912124 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -174627960 a - 1184384449\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-174627960a-1184384449\right){x}$ |
| 32.1-c3 |
32.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$2.88294$ |
$(-23a+156)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$5.183939605$ |
$13.75037163$ |
5.254912124 |
\( 287496 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 11\) , \( 20\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+11{x}+20$ |
| 32.1-c4 |
32.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$2.88294$ |
$(-23a+156)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$5.183939605$ |
$55.00148654$ |
5.254912124 |
\( 287496 \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 34\) , \( 35\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+34{x}+35$ |
| 32.1-d1 |
32.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$2.88294$ |
$(-23a+156)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$27.50074327$ |
1.013690845 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3588 a - 24335\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(3588a-24335\right){x}$ |
| 32.1-d2 |
32.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{46}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$2.88294$ |
$(-23a+156)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$13.75037163$ |
1.013690845 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3588 a + 24335\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(3588a+24335\right){x}$ |
*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.
