| 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 |
| 5625.3-a1 |
5625.3-a |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5625.3 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{2} \cdot 5^{20} \) |
$1.54774$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$0.654920618$ |
0.654920618 |
\( -\frac{102400}{3} \) |
\( \bigl[0\) , \( -1\) , \( i\) , \( -208\) , \( 1256\bigr] \) |
${y}^2+i{y}={x}^{3}-{x}^{2}-208{x}+1256$ |
| 5625.3-a2 |
5625.3-a |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5625.3 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{10} \cdot 5^{4} \) |
$1.54774$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$3.274603091$ |
0.654920618 |
\( \frac{20480}{243} \) |
\( \bigl[0\) , \( -1\) , \( i\) , \( 2\) , \( -4\bigr] \) |
${y}^2+i{y}={x}^{3}-{x}^{2}+2{x}-4$ |
| 5625.3-b1 |
5625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5625.3 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{2} \cdot 5^{32} \) |
$1.54774$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.111785085$ |
1.788561370 |
\( -\frac{117751185817608007}{457763671875} a - \frac{2360548126387992}{152587890625} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2625 i + 9874\) , \( -367500 i - 151477\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-2625i+9874\right){x}-367500i-151477$ |
| 5625.3-b2 |
5625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5625.3 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{2} \cdot 5^{32} \) |
$1.54774$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.111785085$ |
1.788561370 |
\( \frac{117751185817608007}{457763671875} a - \frac{2360548126387992}{152587890625} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( 2625 i + 9875\) , \( -367500 i + 151477\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+\left(2625i+9875\right){x}-367500i+151477$ |
| 5625.3-b3 |
5625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5625.3 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{32} \cdot 5^{14} \) |
$1.54774$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$1$ |
$0.111785085$ |
1.788561370 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2751\) , \( -104477\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-2751{x}-104477$ |
| 5625.3-b4 |
5625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5625.3 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{2} \cdot 5^{14} \) |
$1.54774$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.788561370$ |
1.788561370 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 23\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}+23$ |
| 5625.3-b5 |
5625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5625.3 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{4} \cdot 5^{28} \) |
$1.54774$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$1$ |
$0.223570171$ |
1.788561370 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( 875\) , \( 5227\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}+875{x}+5227$ |
| 5625.3-b6 |
5625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5625.3 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{8} \cdot 5^{20} \) |
$1.54774$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.447140342$ |
1.788561370 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -251\) , \( -727\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-251{x}-727$ |
| 5625.3-b7 |
5625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5625.3 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{4} \cdot 5^{16} \) |
$1.54774$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.894280685$ |
1.788561370 |
\( \frac{13997521}{225} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -125\) , \( -523\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-125{x}-523$ |
| 5625.3-b8 |
5625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5625.3 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{16} \cdot 5^{16} \) |
$1.54774$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.223570171$ |
1.788561370 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -3376\) , \( -75727\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-3376{x}-75727$ |
| 5625.3-b9 |
5625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5625.3 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{2} \cdot 5^{14} \) |
$1.54774$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.447140342$ |
1.788561370 |
\( \frac{56667352321}{15} \) |
\( \bigl[i\) , \( 0\) , \( i\) , \( -2000\) , \( -34273\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-2000{x}-34273$ |
| 5625.3-b10 |
5625.3-b |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5625.3 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{8} \cdot 5^{14} \) |
$1.54774$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{6} \) |
$1$ |
$0.111785085$ |
1.788561370 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -54001\) , \( -4834477\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-54001{x}-4834477$ |
| 5625.3-c1 |
5625.3-c |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5625.3 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{2} \cdot 5^{8} \) |
$1.54774$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.1.3 |
$1$ |
\( 1 \) |
$1$ |
$3.274603091$ |
3.274603091 |
\( -\frac{102400}{3} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -8\) , \( -7\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-8{x}-7$ |
| 5625.3-c2 |
5625.3-c |
$2$ |
$5$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5625.3 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{10} \cdot 5^{16} \) |
$1.54774$ |
$(-a-2), (2a+1), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$5$ |
5B.1.4 |
$1$ |
\( 5 \) |
$1$ |
$0.654920618$ |
3.274603091 |
\( \frac{20480}{243} \) |
\( \bigl[0\) , \( 1\) , \( i\) , \( 42\) , \( -443\bigr] \) |
${y}^2+i{y}={x}^{3}+{x}^{2}+42{x}-443$ |
*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.
