| 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 |
| 63.1-a2 |
63.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( - 3^{20} \cdot 7 \) |
$1.33215$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$6.512163487$ |
1.230683220 |
\( -\frac{1153486390269896663}{301327047} a + \frac{435976874792639720}{43046721} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 115 a - 319\) , \( -1083 a + 3072\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(115a-319\right){x}-1083a+3072$ |
| 63.1-b2 |
63.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( - 3^{20} \cdot 7 \) |
$1.33215$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.985196834$ |
$0.912970485$ |
1.030103091 |
\( -\frac{1153486390269896663}{301327047} a + \frac{435976874792639720}{43046721} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 115 a - 320\) , \( 1198 a - 3392\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(115a-320\right){x}+1198a-3392$ |
| 441.1-a2 |
441.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{20} \cdot 7^{7} \) |
$2.16684$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.651668904$ |
1.970461553 |
\( -\frac{1153486390269896663}{301327047} a + \frac{435976874792639720}{43046721} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -4956 a - 13127\) , \( 2950874 a + 7807239\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4956a-13127\right){x}+2950874a+7807239$ |
| 441.1-f2 |
441.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
441.1 |
\( 3^{2} \cdot 7^{2} \) |
\( - 3^{20} \cdot 7^{7} \) |
$2.16684$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.303337809$ |
1.970461553 |
\( -\frac{1153486390269896663}{301327047} a + \frac{435976874792639720}{43046721} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -4956 a - 13127\) , \( -2950874 a - 7807241\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4956a-13127\right){x}-2950874a-7807241$ |
| 567.1-c2 |
567.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{32} \cdot 7 \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.638508823$ |
$2.170721162$ |
4.329558047 |
\( -\frac{1153486390269896663}{301327047} a + \frac{435976874792639720}{43046721} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 1035 a - 2871\) , \( -29241 a + 82944\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(1035a-2871\right){x}-29241a+82944$ |
| 567.1-l2 |
567.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( - 3^{32} \cdot 7 \) |
$2.30735$ |
$(-a+2), (-a-2), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.304323495$ |
1.840375511 |
\( -\frac{1153486390269896663}{301327047} a + \frac{435976874792639720}{43046721} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 1035 a - 2871\) , \( 29241 a - 82944\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(1035a-2871\right){x}+29241a-82944$ |
*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.
