| 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 |
| 1690.6-a1 |
1690.6-a |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
1690.6 |
\( 2 \cdot 5 \cdot 13^{2} \) |
\( 2 \cdot 5^{10} \cdot 13^{3} \) |
$1.14588$ |
$(a+1), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.074207181$ |
$1.607133521$ |
1.192608490 |
\( -\frac{80398914857}{19531250} a - \frac{197826917099}{19531250} \) |
\( \bigl[1\) , \( -i\) , \( i + 1\) , \( -28 i - 2\) , \( 43 i - 47\bigr] \) |
${y}^2+{x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(-28i-2\right){x}+43i-47$ |
| 8450.9-b1 |
8450.9-b |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8450.9 |
\( 2 \cdot 5^{2} \cdot 13^{2} \) |
\( 2 \cdot 5^{16} \cdot 13^{9} \) |
$1.71349$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.199340379$ |
1.594723038 |
\( -\frac{80398914857}{19531250} a - \frac{197826917099}{19531250} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( 1741 i - 362\) , \( 26365 i + 15070\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}+\left(1741i-362\right){x}+26365i+15070$ |
| 13520.6-a1 |
13520.6-a |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
13520.6 |
\( 2^{4} \cdot 5 \cdot 13^{2} \) |
\( 2^{13} \cdot 5^{10} \cdot 13^{9} \) |
$1.92714$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.222869319$ |
0.891477279 |
\( -\frac{80398914857}{19531250} a - \frac{197826917099}{19531250} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( 604 i - 1288\) , \( 13984 i - 16632\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(604i-1288\right){x}+13984i-16632$ |
| 42250.6-l1 |
42250.6-l |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
42250.6 |
\( 2 \cdot 5^{3} \cdot 13^{2} \) |
\( 2 \cdot 5^{16} \cdot 13^{9} \) |
$2.56227$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$0.199340379$ |
3.986807596 |
\( -\frac{80398914857}{19531250} a - \frac{197826917099}{19531250} \) |
\( \bigl[i\) , \( i + 1\) , \( 0\) , \( -835 i - 1570\) , \( 19373 i + 23386\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-835i-1570\right){x}+19373i+23386$ |
| 67600.9-f1 |
67600.9-f |
$4$ |
$10$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.9 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{13} \cdot 5^{16} \cdot 13^{3} \) |
$2.88174$ |
$(a+1), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.359365980$ |
2.874927842 |
\( -\frac{80398914857}{19531250} a - \frac{197826917099}{19531250} \) |
\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( -309 i - 452\) , \( -4378 i - 3383\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-309i-452\right){x}-4378i-3383$ |
*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.
