| 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-b1 |
5202.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2 \cdot 3^{2} \cdot 17^{7} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.578067282$ |
$0.509184076$ |
1.766055929 |
\( -\frac{1979660058649925}{501126} a - \frac{547309863864799}{167042} \) |
\( \bigl[i\) , \( -i\) , \( 0\) , \( 1584 i + 80\) , \( 15675 i + 18965\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-i{x}^{2}+\left(1584i+80\right){x}+15675i+18965$ |
| 46818.2-e1 |
46818.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
46818.2 |
\( 2 \cdot 3^{4} \cdot 17^{2} \) |
\( 2 \cdot 3^{14} \cdot 17^{7} \) |
$2.62889$ |
$(a+1), (a+4), (a-4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.169728025$ |
2.715648406 |
\( -\frac{1979660058649925}{501126} a - \frac{547309863864799}{167042} \) |
\( \bigl[1\) , \( -1\) , \( i\) , \( 14254 i + 723\) , \( 423947 i + 497800\bigr] \) |
${y}^2+{x}{y}+i{y}={x}^{3}-{x}^{2}+\left(14254i+723\right){x}+423947i+497800$ |
| 88434.2-g1 |
88434.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
88434.2 |
\( 2 \cdot 3^{2} \cdot 17^{3} \) |
\( 2 \cdot 3^{2} \cdot 17^{13} \) |
$3.08193$ |
$(a+1), (a+4), (a-4), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2^{4} \) |
$1$ |
$0.123495278$ |
1.975924450 |
\( -\frac{1979660058649925}{501126} a - \frac{547309863864799}{167042} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -24400 i + 11466\) , \( -225055 i + 1694986\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-24400i+11466\right){x}-225055i+1694986$ |
| 88434.3-i1 |
88434.3-i |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
88434.3 |
\( 2 \cdot 3^{2} \cdot 17^{3} \) |
\( 2 \cdot 3^{2} \cdot 17^{13} \) |
$3.08193$ |
$(a+1), (a+4), (a-4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$0.123495278$ |
5.927773351 |
\( -\frac{1979660058649925}{501126} a - \frac{547309863864799}{167042} \) |
\( \bigl[1\) , \( -i - 1\) , \( i + 1\) , \( -23115 i - 13876\) , \( 1713662 i + 39265\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-23115i-13876\right){x}+1713662i+39265$ |
*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.
