| 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 |
| 72.1-c1 |
72.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{16} \) |
$1.37737$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.325279868$ |
0.878873180 |
\( \frac{207646}{6561} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 190 a + 504\) , \( -16334 a - 43216\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(190a+504\right){x}-16334a-43216$ |
| 72.1-d1 |
72.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{16} \) |
$1.37737$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$5.683508517$ |
2.148164301 |
\( \frac{207646}{6561} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 189 a + 503\) , \( 17022 a + 45035\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(189a+503\right){x}+17022a+45035$ |
| 432.1-c1 |
432.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{22} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.098868579$ |
1.586595513 |
\( \frac{207646}{6561} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -17 a + 40\) , \( -428 a + 1123\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-17a+40\right){x}-428a+1123$ |
| 432.1-g1 |
432.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{22} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.321540817$ |
$2.098868579$ |
4.081241752 |
\( \frac{207646}{6561} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -15 a + 45\) , \( 412 a - 1081\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-15a+45\right){x}+412a-1081$ |
| 432.2-c1 |
432.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.2 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{22} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.098868579$ |
1.586595513 |
\( \frac{207646}{6561} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 15 a + 40\) , \( 427 a + 1123\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(15a+40\right){x}+427a+1123$ |
| 432.2-g1 |
432.2-g |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.2 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{22} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.321540817$ |
$2.098868579$ |
4.081241752 |
\( \frac{207646}{6561} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 15 a + 45\) , \( -412 a - 1081\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(15a+45\right){x}-412a-1081$ |
| 648.1-f1 |
648.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
648.1 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{28} \) |
$2.38568$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.637754311$ |
$0.775093289$ |
3.838342240 |
\( \frac{207646}{6561} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -1690 a + 4481\) , \( 451707 a - 1195095\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1690a+4481\right){x}+451707a-1195095$ |
| 648.1-m1 |
648.1-m |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
648.1 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{28} \) |
$2.38568$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.645289777$ |
$1.894502839$ |
3.696502570 |
\( \frac{207646}{6561} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -1689 a + 4485\) , \( -450610 a + 1192215\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1689a+4485\right){x}-450610a+1192215$ |
*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.
