| 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 |
| 576.4-a2 |
576.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
576.4 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$1.15823$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.270694035$ |
1.374032019 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+{x}$ |
| 2304.5-a2 |
2304.5-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
2304.5 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$1.63798$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$7.270694035$ |
1.374032019 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+{x}$ |
| 4608.4-c2 |
4608.4-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4608.4 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{2} \) |
$1.94790$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.394554452$ |
$5.141157056$ |
3.066752947 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( a - 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(a-2\right){x}$ |
| 4608.7-b2 |
4608.7-b |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4608.7 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{2} \) |
$1.94790$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.394554452$ |
$5.141157056$ |
3.066752947 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a-1\right){x}$ |
| 5184.4-a2 |
5184.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5184.4 |
\( 2^{6} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{14} \) |
$2.00611$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.818877155$ |
$2.423564678$ |
3.000435819 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( -7\bigr] \) |
${y}^2={x}^{3}+6{x}-7$ |
| 9216.5-e2 |
9216.5-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9216.5 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{2} \) |
$2.31645$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.141157056$ |
1.943174717 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( a - 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(a-2\right){x}$ |
| 9216.7-g2 |
9216.7-g |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
9216.7 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{14} \cdot 3^{2} \) |
$2.31645$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.141157056$ |
1.943174717 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-1\right){x}$ |
| 20736.5-c2 |
20736.5-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
20736.5 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{14} \) |
$2.83706$ |
$(a), (-a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.290579554$ |
$2.423564678$ |
4.728793686 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( 7\bigr] \) |
${y}^2={x}^{3}+6{x}+7$ |
| 36864.7-l2 |
36864.7-l |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36864.7 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$3.27596$ |
$(a), (-a+1), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.648228612$ |
$3.635347017$ |
7.125494960 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( 3\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+3{x}+3$ |
| 36864.7-u2 |
36864.7-u |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36864.7 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$3.27596$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.635347017$ |
2.748064039 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 3\) , \( -3\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+3{x}-3$ |
| 41472.4-d2 |
41472.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
41472.4 |
\( 2^{9} \cdot 3^{4} \) |
\( 2^{14} \cdot 3^{14} \) |
$3.37385$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.713719018$ |
2.590899623 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a - 12\) , \( -7 a - 14\bigr] \) |
${y}^2={x}^{3}+\left(6a-12\right){x}-7a-14$ |
| 41472.7-h2 |
41472.7-h |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
41472.7 |
\( 2^{9} \cdot 3^{4} \) |
\( 2^{14} \cdot 3^{14} \) |
$3.37385$ |
$(a), (-a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.713719018$ |
2.590899623 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a - 6\) , \( 7 a - 21\bigr] \) |
${y}^2={x}^{3}+\left(-6a-6\right){x}+7a-21$ |
*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.
