| 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 |
| 77500.2-a1 |
77500.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
77500.2 |
\( 2^{2} \cdot 5^{4} \cdot 31 \) |
\( 2^{2} \cdot 5^{24} \cdot 31^{4} \) |
$2.58241$ |
$(6a-5), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.152440673$ |
0.704093311 |
\( -\frac{18714992594903}{28860031250} a + \frac{17524834976323}{5772006250} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 716 a - 2546\) , \( 15366 a - 30348\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(716a-2546\right){x}+15366a-30348$ |
| 77500.2-a2 |
77500.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
77500.2 |
\( 2^{2} \cdot 5^{4} \cdot 31 \) |
\( 2^{4} \cdot 5^{18} \cdot 31^{2} \) |
$2.58241$ |
$(6a-5), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.304881347$ |
0.704093311 |
\( -\frac{1233998717677}{480500} a + \frac{530744640108}{120125} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 716 a - 2296\) , \( 17116 a - 40348\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(716a-2296\right){x}+17116a-40348$ |
| 77500.2-b1 |
77500.2-b |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
77500.2 |
\( 2^{2} \cdot 5^{4} \cdot 31 \) |
\( 2^{50} \cdot 5^{12} \cdot 31 \) |
$2.58241$ |
$(6a-5), (2), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.3 |
$25$ |
\( 1 \) |
$1$ |
$0.073686357$ |
2.127141908 |
\( \frac{936087656892551}{1040187392} a - \frac{833285178768245}{1040187392} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 18762 a + 13737\) , \( 1281256 a - 2093764\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(18762a+13737\right){x}+1281256a-2093764$ |
| 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 |
\( \frac{24551}{62} a + \frac{66955}{62} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 12 a - 13\) , \( 6 a - 14\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(12a-13\right){x}+6a-14$ |
| 77500.2-b3 |
77500.2-b |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
77500.2 |
\( 2^{2} \cdot 5^{4} \cdot 31 \) |
\( 2^{10} \cdot 5^{12} \cdot 31^{5} \) |
$2.58241$ |
$(6a-5), (2), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5Cs.1.3 |
$1$ |
\( 5 \) |
$1$ |
$0.368431786$ |
2.127141908 |
\( -\frac{511363962461}{916132832} a + \frac{764718499383}{458066416} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -238 a - 138\) , \( 131 a + 1361\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-238a-138\right){x}+131a+1361$ |
*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.
