| 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 |
| 1690.1-a3 |
1690.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1690.1 |
\( 2 \cdot 5 \cdot 13^{2} \) |
\( 2^{10} \cdot 5 \cdot 13^{3} \) |
$1.14588$ |
$(a+1), (-a-2), (-3a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$0.185517953$ |
$3.214267043$ |
1.192608490 |
\( \frac{523313}{160} a + \frac{424661}{40} \) |
\( \bigl[1\) , \( -i\) , \( 0\) , \( -7 i + 1\) , \( 2 i - 8\bigr] \) |
${y}^2+{x}{y}={x}^{3}-i{x}^{2}+\left(-7i+1\right){x}+2i-8$ |
| 8450.1-b3 |
8450.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8450.1 |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{10} \cdot 5^{7} \cdot 13^{9} \) |
$1.71349$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.398680759$ |
1.594723038 |
\( \frac{523313}{160} a + \frac{424661}{40} \) |
\( \bigl[i\) , \( -i + 1\) , \( i\) , \( 451 i + 27\) , \( -2160 i - 2404\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(451i+27\right){x}-2160i-2404$ |
| 13520.1-a3 |
13520.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.1 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{22} \cdot 5 \cdot 13^{9} \) |
$1.92714$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.445738639$ |
0.891477279 |
\( \frac{523313}{160} a + \frac{424661}{40} \) |
\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( 199 i + 302\) , \( -1397 i + 1989\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+{x}^{2}+\left(199i+302\right){x}-1397i+1989$ |
| 42250.7-l3 |
42250.7-l |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.7 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2^{10} \cdot 5^{7} \cdot 13^{9} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.398680759$ |
3.986807596 |
\( \frac{523313}{160} a + \frac{424661}{40} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -152 i + 426\) , \( -3008 i - 1636\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(-152i+426\right){x}-3008i-1636$ |
| 67600.1-f3 |
67600.1-f |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.1 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{22} \cdot 5^{7} \cdot 13^{3} \) |
$2.88174$ |
$(a+1), (-a-2), (-3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.718731960$ |
2.874927842 |
\( \frac{523313}{160} a + \frac{424661}{40} \) |
\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( -61 i + 125\) , \( -484 i - 365\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}-i{x}^{2}+\left(-61i+125\right){x}-484i-365$ |
*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.
