| 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 |
| 50625.1-CMc1 |
50625.1-CMc |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50625.1 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{6} \cdot 5^{20} \) |
$2.32162$ |
$(-2a+1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 3 \) |
$1$ |
$0.554622371$ |
1.921268253 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 781\bigr] \) |
${y}^2+{y}={x}^{3}+781$ |
| 50625.1-CMb1 |
50625.1-CMb |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50625.1 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{6} \cdot 5^{12} \) |
$2.32162$ |
$(-2a+1), (5)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs[2] |
$1$ |
\( 2^{2} \) |
$0.123378097$ |
$1.621725652$ |
3.696619976 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 31\bigr] \) |
${y}^2+{y}={x}^{3}+31$ |
| 50625.1-CMb2 |
50625.1-CMb |
$2$ |
$3$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50625.1 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{10} \cdot 5^{12} \) |
$2.32162$ |
$(-2a+1), (5)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-27$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.123378097$ |
$0.540575217$ |
3.696619976 |
\( -12288000 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -750\) , \( 7906\bigr] \) |
${y}^2+{y}={x}^{3}-750{x}+7906$ |
| 50625.1-CMa1 |
50625.1-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50625.1 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{6} \cdot 5^{8} \) |
$2.32162$ |
$(-2a+1), (5)$ |
0 |
$\Z/3\Z$ |
$\textsf{yes}$ |
$-3$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1[2] |
$1$ |
\( 3 \) |
$1$ |
$2.773111858$ |
1.067371251 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 6\bigr] \) |
${y}^2+{y}={x}^{3}+6$ |
| 50625.1-a1 |
50625.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50625.1 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{10} \cdot 5^{16} \) |
$2.32162$ |
$(-2a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$5$ |
5Nn.1.1.1 |
$1$ |
\( 3 \) |
$0.508507719$ |
$0.641413358$ |
2.259728010 |
\( 1875 \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 117 a\) , \( 166\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+117a{x}+166$ |
| 50625.1-b1 |
50625.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50625.1 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{10} \cdot 5^{4} \) |
$2.32162$ |
$(-2a+1), (5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$5$ |
5Nn.1.1.1 |
$1$ |
\( 3 \) |
$0.131955364$ |
$3.207066792$ |
2.931944020 |
\( 1875 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-5{x}+2$ |
| 50625.1-e1 |
50625.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50625.1 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{10} \cdot 5^{16} \) |
$2.32162$ |
$(-2a+1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cn |
$1$ |
\( 2^{2} \) |
$1$ |
$0.644047451$ |
2.974727755 |
\( -\frac{12288}{25} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -75 a + 75\) , \( 531\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-75a+75\right){x}+531$ |
| 50625.1-f1 |
50625.1-f |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50625.1 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{10} \cdot 5^{4} \) |
$2.32162$ |
$(-2a+1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 7$ |
2Cn, 7B |
$1$ |
\( 1 \) |
$1$ |
$1.782026516$ |
2.057706977 |
\( 2260440 a + 2175405 \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 52 a - 65\) , \( 183 a - 129\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(52a-65\right){x}+183a-129$ |
| 50625.1-f2 |
50625.1-f |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50625.1 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{10} \cdot 5^{4} \) |
$2.32162$ |
$(-2a+1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 7$ |
2Cn, 7B |
$1$ |
\( 1 \) |
$1$ |
$1.782026516$ |
2.057706977 |
\( -2260440 a + 4435845 \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -13 a + 65\) , \( -184 a + 55\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-13a+65\right){x}-184a+55$ |
| 50625.1-g1 |
50625.1-g |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50625.1 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{10} \cdot 5^{16} \) |
$2.32162$ |
$(-2a+1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 7$ |
2Cn, 7B |
$1$ |
\( 3^{2} \) |
$1$ |
$0.356405303$ |
3.703872559 |
\( 2260440 a + 2175405 \) |
\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -1618 a + 305\) , \( 24281 a - 17740\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-1618a+305\right){x}+24281a-17740$ |
| 50625.1-g2 |
50625.1-g |
$2$ |
$7$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50625.1 |
\( 3^{4} \cdot 5^{4} \) |
\( 3^{10} \cdot 5^{16} \) |
$2.32162$ |
$(-2a+1), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 7$ |
2Cn, 7B |
$1$ |
\( 3^{2} \) |
$1$ |
$0.356405303$ |
3.703872559 |
\( -2260440 a + 4435845 \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 1616 a - 1312\) , \( -24282 a + 6541\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1616a-1312\right){x}-24282a+6541$ |
*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.
