| 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-b2 |
5202.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 17^{8} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.289033641$ |
$1.018368152$ |
1.766055929 |
\( \frac{9390341072075}{144825414} a - \frac{6456168132412}{217238121} \) |
\( \bigl[1\) , \( i\) , \( 0\) , \( 99 i + 5\) , \( -240 i - 320\bigr] \) |
${y}^2+{x}{y}={x}^{3}+i{x}^{2}+\left(99i+5\right){x}-240i-320$ |
| 46818.2-e2 |
46818.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
46818.2 |
\( 2 \cdot 3^{4} \cdot 17^{2} \) |
\( 2^{2} \cdot 3^{16} \cdot 17^{8} \) |
$2.62889$ |
$(a+1), (a+4), (a-4), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$0.339456050$ |
2.715648406 |
\( \frac{9390341072075}{144825414} a - \frac{6456168132412}{217238121} \) |
\( \bigl[1\) , \( -1\) , \( i\) , \( 889 i + 48\) , \( 6527 i + 7750\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}-{x}^{2}+\left(889i+48\right){x}+6527i+7750$ |
| 88434.2-g2 |
88434.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
88434.2 |
\( 2 \cdot 3^{2} \cdot 17^{3} \) |
\( 2^{2} \cdot 3^{4} \cdot 17^{14} \) |
$3.08193$ |
$(a+1), (a+4), (a-4), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$0.246990556$ |
1.975924450 |
\( \frac{9390341072075}{144825414} a - \frac{6456168132412}{217238121} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -1525 i + 711\) , \( -3835 i + 26806\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-1525i+711\right){x}-3835i+26806$ |
| 88434.3-i2 |
88434.3-i |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
88434.3 |
\( 2 \cdot 3^{2} \cdot 17^{3} \) |
\( 2^{2} \cdot 3^{4} \cdot 17^{14} \) |
$3.08193$ |
$(a+1), (a+4), (a-4), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \cdot 3 \) |
$1$ |
$0.246990556$ |
5.927773351 |
\( \frac{9390341072075}{144825414} a - \frac{6456168132412}{217238121} \) |
\( \bigl[1\) , \( -i - 1\) , \( i + 1\) , \( -1440 i - 871\) , \( 27347 i + 250\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-1440i-871\right){x}+27347i+250$ |
*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.
