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
31.1-a5
31.1-a
$6$
$8$
\(\Q(\zeta_{15})^+\)
$4$
$[4, 0]$
31.1
\( 31 \)
\( 31^{4} \)
$4.60400$
$(a^3+2a^2-3a-3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2 \)
$1$
$226.2402485$
0.843147624
\( -\frac{2933497938285}{923521} a^{3} + \frac{9133676668039}{923521} a^{2} - \frac{6067822613957}{923521} a - \frac{1204128338708}{923521} \)
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 1\) , \( -22 a^{3} - 21 a^{2} + 60 a + 12\) , \( -77 a^{3} - 67 a^{2} + 195 a + 43\bigr] \)
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+{y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(-22a^{3}-21a^{2}+60a+12\right){x}-77a^{3}-67a^{2}+195a+43$
31.1-b5
31.1-b
$6$
$8$
\(\Q(\zeta_{15})^+\)
$4$
$[4, 0]$
31.1
\( 31 \)
\( 31^{4} \)
$4.60400$
$(a^3+2a^2-3a-3)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2 \)
$1$
$757.6135842$
0.705864781
\( -\frac{2933497938285}{923521} a^{3} + \frac{9133676668039}{923521} a^{2} - \frac{6067822613957}{923521} a - \frac{1204128338708}{923521} \)
\( \bigl[a^{2} - 2\) , \( -a^{2} + 1\) , \( 0\) , \( -4\) , \( -a^{3} + 4 a^{2} + 4 a - 7\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(-a^{2}+1\right){x}^{2}-4{x}-a^{3}+4a^{2}+4a-7$
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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.