| 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 |
| 87616.2-a1 |
87616.2-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87616.2 |
\( 2^{6} \cdot 37^{2} \) |
\( 2^{16} \cdot 37^{4} \) |
$2.66284$ |
$(-7a+4), (-7a+3), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.118829960$ |
$1.658179863$ |
2.730286398 |
\( \frac{10649600}{50653} a + \frac{3830784}{50653} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 11 a - 7\) , \( 28 a - 31\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(11a-7\right){x}+28a-31$ |
| 87616.2-b1 |
87616.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87616.2 |
\( 2^{6} \cdot 37^{2} \) |
\( 2^{16} \cdot 37^{2} \) |
$2.66284$ |
$(-7a+4), (-7a+3), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.113678972$ |
$2.038746731$ |
4.281862998 |
\( \frac{16000000}{37} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -33\) , \( 85\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-33{x}+85$ |
| 87616.2-c1 |
87616.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87616.2 |
\( 2^{6} \cdot 37^{2} \) |
\( 2^{16} \cdot 37^{2} \) |
$2.66284$ |
$(-7a+4), (-7a+3), (2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.096991529$ |
$2.730485956$ |
4.892863548 |
\( \frac{351232}{37} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -9\) , \( 13\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-9{x}+13$ |
| 87616.2-d1 |
87616.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87616.2 |
\( 2^{6} \cdot 37^{2} \) |
\( 2^{16} \cdot 37^{4} \) |
$2.66284$ |
$(-7a+4), (-7a+3), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$0.118829960$ |
$1.658179863$ |
2.730286398 |
\( -\frac{10649600}{50653} a + \frac{14480384}{50653} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 7 a - 11\) , \( -28 a - 3\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(7a-11\right){x}-28a-3$ |
| 87616.2-e1 |
87616.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87616.2 |
\( 2^{6} \cdot 37^{2} \) |
\( 2^{8} \cdot 37^{3} \) |
$2.66284$ |
$(-7a+4), (-7a+3), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.308343085$ |
$3.562351090$ |
5.073413882 |
\( -\frac{228096}{1369} a + \frac{207360}{1369} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -a + 1\) , \( 4 a - 2\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a+1\right){x}+4a-2$ |
| 87616.2-e2 |
87616.2-e |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87616.2 |
\( 2^{6} \cdot 37^{2} \) |
\( 2^{16} \cdot 37^{3} \) |
$2.66284$ |
$(-7a+4), (-7a+3), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.308343085$ |
$1.781175545$ |
5.073413882 |
\( -\frac{86662224}{1369} a + \frac{16349904}{1369} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -16 a + 36\) , \( 56 a\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-16a+36\right){x}+56a$ |
| 87616.2-f1 |
87616.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87616.2 |
\( 2^{6} \cdot 37^{2} \) |
\( 2^{16} \cdot 37^{3} \) |
$2.66284$ |
$(-7a+4), (-7a+3), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.308343085$ |
$1.781175545$ |
5.073413882 |
\( \frac{86662224}{1369} a - \frac{70312320}{1369} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 20 a - 36\) , \( -56 a + 56\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(20a-36\right){x}-56a+56$ |
| 87616.2-f2 |
87616.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
87616.2 |
\( 2^{6} \cdot 37^{2} \) |
\( 2^{8} \cdot 37^{3} \) |
$2.66284$ |
$(-7a+4), (-7a+3), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.308343085$ |
$3.562351090$ |
5.073413882 |
\( \frac{228096}{1369} a - \frac{20736}{1369} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -1\) , \( -4 a + 2\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-{x}-4a+2$ |
*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.
