| 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-c6 |
72.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \) |
$1.37737$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.325279868$ |
0.878873180 |
\( \frac{3065617154}{9} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -4610 a - 12196\) , \( -286494 a - 757992\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-4610a-12196\right){x}-286494a-757992$ |
| 72.1-d6 |
72.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \) |
$1.37737$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$22.73403407$ |
2.148164301 |
\( \frac{3065617154}{9} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -4611 a - 12197\) , \( 269682 a + 713511\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4611a-12197\right){x}+269682a+713511$ |
| 432.1-c6 |
432.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{10} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.197737158$ |
1.586595513 |
\( \frac{3065617154}{9} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 383 a - 1060\) , \( -6584 a + 17323\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(383a-1060\right){x}-6584a+17323$ |
| 432.1-g6 |
432.1-g |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.1 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{10} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.286163271$ |
$4.197737158$ |
4.081241752 |
\( \frac{3065617154}{9} \) |
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 385 a - 1055\) , \( 6968 a - 18381\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(385a-1055\right){x}+6968a-18381$ |
| 432.2-c6 |
432.2-c |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.2 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{10} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.197737158$ |
1.586595513 |
\( \frac{3065617154}{9} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -385 a - 1060\) , \( 6583 a + 17323\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-385a-1060\right){x}+6583a+17323$ |
| 432.2-g6 |
432.2-g |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
432.2 |
\( 2^{4} \cdot 3^{3} \) |
\( 2^{10} \cdot 3^{10} \) |
$2.15570$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.286163271$ |
$4.197737158$ |
4.081241752 |
\( \frac{3065617154}{9} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -385 a - 1055\) , \( -6968 a - 18381\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-385a-1055\right){x}-6968a-18381$ |
| 648.1-f6 |
648.1-f |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
648.1 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{16} \) |
$2.38568$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1.637754311$ |
$0.775093289$ |
3.838342240 |
\( \frac{3065617154}{9} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -41505 a - 109815\) , \( -7584046 a - 20065501\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-41505a-109815\right){x}-7584046a-20065501$ |
| 648.1-m6 |
648.1-m |
$6$ |
$8$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
648.1 |
\( 2^{3} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{16} \) |
$2.38568$ |
$(a+3), (-a+2), (-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.645289777$ |
$7.578011356$ |
3.696502570 |
\( \frac{3065617154}{9} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -41506 a - 109819\) , \( 7391211 a + 19555309\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-41506a-109819\right){x}+7391211a+19555309$ |
*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.
