| 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 |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
87616.2 |
\( 2^{6} \cdot 37^{2} \) |
\( 2^{12} \cdot 37^{2} \) |
$3.07478$ |
$(a+1), (a+6), (a-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.211417693$ |
$1.908316256$ |
3.227614565 |
\( \frac{337153536}{37} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 58\) , \( -170 i\bigr] \) |
${y}^2={x}^{3}+58{x}-170i$ |
| 87616.2-b1 |
87616.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
87616.2 |
\( 2^{6} \cdot 37^{2} \) |
\( 2^{12} \cdot 37^{6} \) |
$3.07478$ |
$(a+1), (a+6), (a-6)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2 \cdot 5 \) |
$0.119680982$ |
$1.129937894$ |
5.409283089 |
\( -\frac{33742443520}{69343957} a + \frac{85490406912}{69343957} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 34 i - 6\) , \( -6 i + 68\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(34i-6\right){x}-6i+68$ |
| 87616.2-b2 |
87616.2-b |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
87616.2 |
\( 2^{6} \cdot 37^{2} \) |
\( 2^{12} \cdot 37^{6} \) |
$3.07478$ |
$(a+1), (a+6), (a-6)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$5$ |
5B |
$1$ |
\( 2 \cdot 5 \) |
$0.119680982$ |
$1.129937894$ |
5.409283089 |
\( \frac{33742443520}{69343957} a + \frac{85490406912}{69343957} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -34 i - 6\) , \( 6 i + 68\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-34i-6\right){x}+6i+68$ |
| 87616.2-c1 |
87616.2-c |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
87616.2 |
\( 2^{6} \cdot 37^{2} \) |
\( 2^{12} \cdot 37^{2} \) |
$3.07478$ |
$(a+1), (a+6), (a-6)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2 \) |
$0.212119068$ |
$3.766152088$ |
6.390981384 |
\( \frac{64000}{37} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 3\) , \( i\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+3{x}+i$ |
| 87616.2-d1 |
87616.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
87616.2 |
\( 2^{6} \cdot 37^{2} \) |
\( 2^{6} \cdot 37^{5} \) |
$3.07478$ |
$(a+1), (a+6), (a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.873954024$ |
$2.010657031$ |
5.778535867 |
\( -\frac{4526180208}{1874161} a - \frac{9479776248}{1874161} \) |
\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -16 i - 1\) , \( -20 i + 24\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+i{x}^{2}+\left(-16i-1\right){x}-20i+24$ |
| 87616.2-d2 |
87616.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
87616.2 |
\( 2^{6} \cdot 37^{2} \) |
\( 2^{6} \cdot 37^{5} \) |
$3.07478$ |
$(a+1), (a+6), (a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.873954024$ |
$2.010657031$ |
5.778535867 |
\( \frac{4526180208}{1874161} a - \frac{9479776248}{1874161} \) |
\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 15 i - 1\) , \( 19 i + 9\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+i{x}^{2}+\left(15i-1\right){x}+19i+9$ |
| 87616.2-d3 |
87616.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
87616.2 |
\( 2^{6} \cdot 37^{2} \) |
\( 2^{12} \cdot 37^{4} \) |
$3.07478$ |
$(a+1), (a+6), (a-6)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.436977012$ |
$2.010657031$ |
5.778535867 |
\( -\frac{2299968}{1369} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 11\) , \( -20 i\bigr] \) |
${y}^2={x}^{3}+11{x}-20i$ |
| 87616.2-d4 |
87616.2-d |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
87616.2 |
\( 2^{6} \cdot 37^{2} \) |
\( 2^{12} \cdot 37^{2} \) |
$3.07478$ |
$(a+1), (a+6), (a-6)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.873954024$ |
$2.010657031$ |
5.778535867 |
\( \frac{203297472}{37} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -49\) , \( 132\bigr] \) |
${y}^2={x}^{3}-49{x}+132$ |
| 87616.2-e1 |
87616.2-e |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
87616.2 |
\( 2^{6} \cdot 37^{2} \) |
\( 2^{12} \cdot 37^{6} \) |
$3.07478$ |
$(a+1), (a+6), (a-6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3Cn |
$4$ |
\( 2 \) |
$1$ |
$0.746769312$ |
5.974154499 |
\( \frac{31077609984}{50653} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 262\) , \( 1630 i\bigr] \) |
${y}^2={x}^{3}+262{x}+1630i$ |
*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.
