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
31.3-a4
31.3-a
$6$
$8$
\(\Q(\zeta_{15})^+\)
$4$
$[4, 0]$
31.3
\( 31 \)
\( 31^{4} \)
$4.60400$
$(-2a^3-2a^2+6a+3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2 \)
$1$
$226.2402485$
0.843147624
\( \frac{17801814367097}{923521} a^{3} + \frac{14868316428812}{923521} a^{2} - \frac{44271766433252}{923521} a - \frac{9739909921969}{923521} \)
\( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 25 a^{3} + 4 a^{2} - 97 a - 18\) , \( 82 a^{3} + 20 a^{2} - 308 a - 64\bigr] \)
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(25a^{3}+4a^{2}-97a-18\right){x}+82a^{3}+20a^{2}-308a-64$
31.3-b4
31.3-b
$6$
$8$
\(\Q(\zeta_{15})^+\)
$4$
$[4, 0]$
31.3
\( 31 \)
\( 31^{4} \)
$4.60400$
$(-2a^3-2a^2+6a+3)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2 \)
$1$
$757.6135842$
0.705864781
\( \frac{17801814367097}{923521} a^{3} + \frac{14868316428812}{923521} a^{2} - \frac{44271766433252}{923521} a - \frac{9739909921969}{923521} \)
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -4\) , \( -a^{2} + 4 a + 4\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}-4{x}-a^{2}+4a+4$
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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.