| 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 |
| 124.2-a2 |
124.2-a |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
124.2 |
\( 2^{2} \cdot 31 \) |
\( 2^{2} \cdot 31 \) |
$0.51648$ |
$(6a-5), (2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$9.210794651$ |
0.425428381 |
\( \frac{24551}{62} a + \frac{66955}{62} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -a + 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a+1\right){x}$ |
| 7936.2-d2 |
7936.2-d |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7936.2 |
\( 2^{8} \cdot 31 \) |
\( 2^{26} \cdot 31 \) |
$1.46083$ |
$(6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.115294444$ |
$2.302698662$ |
2.452476457 |
\( \frac{24551}{62} a + \frac{66955}{62} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 8\) , \( 4\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+8{x}+4$ |
| 20956.2-b2 |
20956.2-b |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
20956.2 |
\( 2^{2} \cdot 13^{2} \cdot 31 \) |
\( 2^{2} \cdot 13^{6} \cdot 31 \) |
$1.86220$ |
$(-4a+1), (6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$0.278764670$ |
$2.554614800$ |
3.289216924 |
\( \frac{24551}{62} a + \frac{66955}{62} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( -7 a + 4\) , \( -6 a + 1\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-7a+4\right){x}-6a+1$ |
| 20956.6-c2 |
20956.6-c |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
20956.6 |
\( 2^{2} \cdot 13^{2} \cdot 31 \) |
\( 2^{2} \cdot 13^{6} \cdot 31 \) |
$1.86220$ |
$(4a-3), (6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$2.554614800$ |
2.949815085 |
\( \frac{24551}{62} a + \frac{66955}{62} \) |
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -4 a - 3\) , \( 8 a - 4\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a-3\right){x}+8a-4$ |
| 34596.3-d2 |
34596.3-d |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
34596.3 |
\( 2^{2} \cdot 3^{2} \cdot 31^{2} \) |
\( 2^{2} \cdot 3^{6} \cdot 31^{7} \) |
$2.11084$ |
$(-2a+1), (6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$0.955114912$ |
2.205743407 |
\( \frac{24551}{62} a + \frac{66955}{62} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 37 a + 16\) , \( 49 a + 23\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(37a+16\right){x}+49a+23$ |
| 54684.2-d2 |
54684.2-d |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
54684.2 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 31 \) |
\( 2^{2} \cdot 3^{6} \cdot 7^{6} \cdot 31 \) |
$2.36681$ |
$(-2a+1), (-3a+1), (6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$0.420856605$ |
$2.009960176$ |
3.907067914 |
\( \frac{24551}{62} a + \frac{66955}{62} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -9 a - 4\) , \( -8 a + 5\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-9a-4\right){x}-8a+5$ |
| 54684.6-b2 |
54684.6-b |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
54684.6 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 31 \) |
\( 2^{2} \cdot 3^{6} \cdot 7^{6} \cdot 31 \) |
$2.36681$ |
$(-2a+1), (3a-2), (6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$2.009960176$ |
2.320902097 |
\( \frac{24551}{62} a + \frac{66955}{62} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 8 a - 13\) , \( a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(8a-13\right){x}+a-1$ |
| 71424.2-c2 |
71424.2-c |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
71424.2 |
\( 2^{8} \cdot 3^{2} \cdot 31 \) |
\( 2^{26} \cdot 3^{6} \cdot 31 \) |
$2.53023$ |
$(-2a+1), (6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.280384421$ |
$1.329463692$ |
3.443417772 |
\( \frac{24551}{62} a + \frac{66955}{62} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -23 a + 25\) , \( 25 a + 12\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-23a+25\right){x}+25a+12$ |
| 71424.2-g2 |
71424.2-g |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
71424.2 |
\( 2^{8} \cdot 3^{2} \cdot 31 \) |
\( 2^{26} \cdot 3^{6} \cdot 31 \) |
$2.53023$ |
$(-2a+1), (6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$1.329463692$ |
3.070264883 |
\( \frac{24551}{62} a + \frac{66955}{62} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -24\) , \( -24 a + 12\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-24{x}-24a+12$ |
| 77500.2-b2 |
77500.2-b |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
77500.2 |
\( 2^{2} \cdot 5^{4} \cdot 31 \) |
\( 2^{2} \cdot 5^{12} \cdot 31 \) |
$2.58241$ |
$(6a-5), (2), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.4 |
$1$ |
\( 1 \) |
$1$ |
$1.842158930$ |
2.127141908 |
\( \frac{24551}{62} a + \frac{66955}{62} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 12 a - 13\) , \( 6 a - 14\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(12a-13\right){x}+6a-14$ |
| 126976.2-e2 |
126976.2-e |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.2 |
\( 2^{12} \cdot 31 \) |
\( 2^{38} \cdot 31 \) |
$2.92166$ |
$(6a-5), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2^{2} \) |
$0.350530872$ |
$1.151349331$ |
3.728144549 |
\( \frac{24551}{62} a + \frac{66955}{62} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 32 a - 33\) , \( -32 a + 65\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(32a-33\right){x}-32a+65$ |
| 126976.2-f2 |
126976.2-f |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
126976.2 |
\( 2^{12} \cdot 31 \) |
\( 2^{38} \cdot 31 \) |
$2.92166$ |
$(6a-5), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$1.151349331$ |
2.658927385 |
\( \frac{24551}{62} a + \frac{66955}{62} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -33 a + 1\) , \( 32 a - 65\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-33a+1\right){x}+32a-65$ |
*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.
