| 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 |
| 13520.5-b3 |
13520.5-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.5 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{6} \cdot 13^{10} \) |
$1.92714$ |
$(a+1), (2a+1), (-3a-2), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$0.542206631$ |
2.439929842 |
\( \frac{303358645539264}{75418890625} a - \frac{163513993683952}{75418890625} \) |
\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( 115 i - 159\) , \( 788 i - 781\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(115i-159\right){x}+788i-781$ |
| 33800.8-b3 |
33800.8-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
33800.8 |
\( 2^{3} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{4} \cdot 5^{12} \cdot 13^{10} \) |
$2.42325$ |
$(a+1), (2a+1), (-3a-2), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \cdot 3 \) |
$0.563717299$ |
$0.242482177$ |
3.280593557 |
\( \frac{303358645539264}{75418890625} a - \frac{163513993683952}{75418890625} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -987 i + 12\) , \( 8097 i - 10180\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-987i+12\right){x}+8097i-10180$ |
| 87880.6-b3 |
87880.6-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
87880.6 |
\( 2^{3} \cdot 5 \cdot 13^{3} \) |
\( 2^{4} \cdot 5^{6} \cdot 13^{16} \) |
$3.07710$ |
$(a+1), (2a+1), (-3a-2), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \cdot 3 \) |
$1$ |
$0.150381062$ |
1.804572750 |
\( \frac{303358645539264}{75418890625} a - \frac{163513993683952}{75418890625} \) |
\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( 2492 i + 600\) , \( 30722 i + 46390\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(2492i+600\right){x}+30722i+46390$ |
| 87880.7-c3 |
87880.7-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
87880.7 |
\( 2^{3} \cdot 5 \cdot 13^{3} \) |
\( 2^{4} \cdot 5^{6} \cdot 13^{16} \) |
$3.07710$ |
$(a+1), (2a+1), (-3a-2), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$8.806602378$ |
$0.150381062$ |
5.297384891 |
\( \frac{303358645539264}{75418890625} a - \frac{163513993683952}{75418890625} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -1329 i - 2192\) , \( 44351 i + 31432\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-1329i-2192\right){x}+44351i+31432$ |
*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.
