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 |
100156.4-b2 |
100156.4-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
100156.4 |
\( 2^{2} \cdot 7^{3} \cdot 73 \) |
\( 2^{4} \cdot 7^{10} \cdot 73^{2} \) |
$2.75339$ |
$(-3a+1), (3a-2), (9a-8), (2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.596187144$ |
1.376835233 |
\( \frac{5321822571516}{1827847} a + \frac{2824357089119}{7311388} \) |
\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -489 a + 541\) , \( 791 a + 3849\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-489a+541\right){x}+791a+3849$ |
100156.6-f2 |
100156.6-f |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
100156.6 |
\( 2^{2} \cdot 7^{3} \cdot 73 \) |
\( 2^{4} \cdot 7^{10} \cdot 73^{2} \) |
$2.75339$ |
$(-3a+1), (3a-2), (9a-8), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.809998644$ |
$0.596187144$ |
6.691408034 |
\( \frac{5321822571516}{1827847} a + \frac{2824357089119}{7311388} \) |
\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -119 a + 567\) , \( 5007 a - 1017\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-119a+567\right){x}+5007a-1017$ |
128772.4-b2 |
128772.4-b |
$2$ |
$2$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
128772.4 |
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 73 \) |
\( 2^{4} \cdot 3^{6} \cdot 7^{4} \cdot 73^{2} \) |
$2.93194$ |
$(-2a+1), (-3a+1), (3a-2), (9a-8), (2)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.910690905$ |
2.103150558 |
\( \frac{5321822571516}{1827847} a + \frac{2824357089119}{7311388} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( -115 a - 141\) , \( 853 a + 523\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-115a-141\right){x}+853a+523$ |
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*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.