| 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 |
| 392.1-a1 |
392.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$1.94790$ |
$(-a+2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$22.75712104$ |
4.645277881 |
\( -\frac{4}{7} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -3\) , \( -1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-3{x}-1$ |
| 392.1-a2 |
392.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{4} \) |
$1.94790$ |
$(-a+2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$22.75712104$ |
4.645277881 |
\( \frac{3543122}{49} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -13\) , \( 9\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-13{x}+9$ |
| 392.1-b1 |
392.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{2} \) |
$1.94790$ |
$(-a+2), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.747807462$ |
$7.189921948$ |
2.565146328 |
\( -\frac{4}{7} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -2 a - 2\) , \( -100 a - 244\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a-2\right){x}-100a-244$ |
| 392.1-b2 |
392.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{4} \) |
$1.94790$ |
$(-a+2), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.873903731$ |
$7.189921948$ |
2.565146328 |
\( \frac{3543122}{49} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 202 a - 492\) , \( 2280 a - 5584\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(202a-492\right){x}+2280a-5584$ |
| 392.1-c1 |
392.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$1.94790$ |
$(-a+2), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$24.47471212$ |
2.497939845 |
\( \frac{432}{7} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 5 a + 10\) , \( 52 a + 126\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(5a+10\right){x}+52a+126$ |
| 392.1-c2 |
392.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{8} \) |
$1.94790$ |
$(-a+2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$6.118678030$ |
2.497939845 |
\( \frac{11090466}{2401} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -295 a - 725\) , \( -3563 a - 8729\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-295a-725\right){x}-3563a-8729$ |
| 392.1-c3 |
392.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{4} \) |
$1.94790$ |
$(-a+2), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$24.47471212$ |
2.497939845 |
\( \frac{740772}{49} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 95 a - 235\) , \( -695 a + 1701\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(95a-235\right){x}-695a+1701$ |
| 392.1-c4 |
392.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{2} \) |
$1.94790$ |
$(-a+2), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$24.47471212$ |
2.497939845 |
\( \frac{1443468546}{7} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -1495 a - 3665\) , \( 48505 a + 118811\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-1495a-3665\right){x}+48505a+118811$ |
| 392.1-d1 |
392.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$1.94790$ |
$(-a+2), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.069108576$ |
$10.54517411$ |
2.301282567 |
\( \frac{432}{7} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}$ |
| 392.1-d2 |
392.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{8} \) |
$1.94790$ |
$(-a+2), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.069108576$ |
$10.54517411$ |
2.301282567 |
\( \frac{11090466}{2401} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -14\) , \( 10\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-14{x}+10$ |
| 392.1-d3 |
392.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{8} \cdot 7^{4} \) |
$1.94790$ |
$(-a+2), (7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$2.138217153$ |
$10.54517411$ |
2.301282567 |
\( \frac{740772}{49} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -4\) , \( -6\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-4{x}-6$ |
| 392.1-d4 |
392.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{2} \) |
$1.94790$ |
$(-a+2), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$4.276434307$ |
$2.636293528$ |
2.301282567 |
\( \frac{1443468546}{7} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -74\) , \( -286\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-74{x}-286$ |
*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.
