| 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 |
| 77500.1-a1 |
77500.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
77500.1 |
\( 2^{2} \cdot 5^{4} \cdot 31 \) |
\( 2^{2} \cdot 5^{24} \cdot 31^{4} \) |
$2.58241$ |
$(-6a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.152440673$ |
0.704093311 |
\( \frac{18714992594903}{28860031250} a + \frac{34454591143356}{14430015625} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 2546 a - 716\) , \( -15366 a - 14982\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(2546a-716\right){x}-15366a-14982$ |
| 77500.1-a2 |
77500.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
77500.1 |
\( 2^{2} \cdot 5^{4} \cdot 31 \) |
\( 2^{4} \cdot 5^{18} \cdot 31^{2} \) |
$2.58241$ |
$(-6a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.304881347$ |
0.704093311 |
\( \frac{1233998717677}{480500} a + \frac{177795968551}{96100} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 2296 a - 716\) , \( -17116 a - 23232\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(2296a-716\right){x}-17116a-23232$ |
| 77500.1-b1 |
77500.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
77500.1 |
\( 2^{2} \cdot 5^{4} \cdot 31 \) |
\( 2^{10} \cdot 5^{12} \cdot 31^{5} \) |
$2.58241$ |
$(-6a+1), (2), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5Cs.1.3 |
$1$ |
\( 5 \) |
$1$ |
$0.368431786$ |
2.127141908 |
\( \frac{511363962461}{916132832} a + \frac{1018073036305}{916132832} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 137 a + 238\) , \( -132 a + 1492\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(137a+238\right){x}-132a+1492$ |
| 77500.1-b2 |
77500.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
77500.1 |
\( 2^{2} \cdot 5^{4} \cdot 31 \) |
\( 2^{2} \cdot 5^{12} \cdot 31 \) |
$2.58241$ |
$(-6a+1), (2), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.4 |
$1$ |
\( 1 \) |
$1$ |
$1.842158930$ |
2.127141908 |
\( -\frac{24551}{62} a + \frac{45753}{31} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 12 a - 12\) , \( -7 a - 8\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(12a-12\right){x}-7a-8$ |
| 77500.1-b3 |
77500.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
77500.1 |
\( 2^{2} \cdot 5^{4} \cdot 31 \) |
\( 2^{50} \cdot 5^{12} \cdot 31 \) |
$2.58241$ |
$(-6a+1), (2), (5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.1.3 |
$25$ |
\( 1 \) |
$1$ |
$0.073686357$ |
2.127141908 |
\( -\frac{936087656892551}{1040187392} a + \frac{51401239062153}{520093696} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -13738 a - 18762\) , \( -1281257 a - 812508\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-13738a-18762\right){x}-1281257a-812508$ |
*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.
