| 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 |
| 5202.2-e5 |
5202.2-e |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{8} \cdot 17^{8} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{8} \) |
$0.956745442$ |
$0.367508294$ |
2.812895085 |
\( \frac{576615941610337}{27060804} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -1734\) , \( -27936\bigr] \) |
${y}^2+{x}{y}={x}^{3}-1734{x}-27936$ |
| 46818.2-b5 |
46818.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
46818.2 |
\( 2 \cdot 3^{4} \cdot 17^{2} \) |
\( 2^{4} \cdot 3^{20} \cdot 17^{8} \) |
$2.62889$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$8.034349782$ |
$0.122502764$ |
3.936920247 |
\( \frac{576615941610337}{27060804} \) |
\( \bigl[i\) , \( 1\) , \( 0\) , \( -15606\) , \( -754272\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+{x}^{2}-15606{x}-754272$ |
| 88434.2-b5 |
88434.2-b |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
88434.2 |
\( 2 \cdot 3^{2} \cdot 17^{3} \) |
\( 2^{4} \cdot 3^{8} \cdot 17^{14} \) |
$3.08193$ |
$(a+1), (a+4), (a-4), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{6} \) |
$1$ |
$0.089133853$ |
1.426141662 |
\( \frac{576615941610337}{27060804} \) |
\( \bigl[1\) , \( -i\) , \( 0\) , \( 13872 i + 26010\) , \( -1452672 i + 1312992\bigr] \) |
${y}^2+{x}{y}={x}^{3}-i{x}^{2}+\left(13872i+26010\right){x}-1452672i+1312992$ |
| 88434.3-d5 |
88434.3-d |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
88434.3 |
\( 2 \cdot 3^{2} \cdot 17^{3} \) |
\( 2^{4} \cdot 3^{8} \cdot 17^{14} \) |
$3.08193$ |
$(a+1), (a+4), (a-4), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{6} \) |
$1$ |
$0.089133853$ |
1.426141662 |
\( \frac{576615941610337}{27060804} \) |
\( \bigl[i\) , \( -i\) , \( 0\) , \( -13872 i + 26010\) , \( -1452672 i - 1312992\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-i{x}^{2}+\left(-13872i+26010\right){x}-1452672i-1312992$ |
*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.
