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-a1
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
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$226.2402485$
0.843147624
\( -\frac{3352161032683862028986803952}{923521} a^{3} + \frac{9909977575470350951831216400}{923521} a^{2} - \frac{5978197446809240162656682401}{923521} a - \frac{1713525152117869864310632982}{923521} \)
\( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 495 a^{3} + 69 a^{2} - 1642 a - 353\) , \( -7129 a^{3} - 1543 a^{2} + 24030 a + 5034\bigr] \)
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(495a^{3}+69a^{2}-1642a-353\right){x}-7129a^{3}-1543a^{2}+24030a+5034$
31.3-b1
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
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$16$
\( 2 \)
$1$
$2.959428063$
0.705864781
\( -\frac{3352161032683862028986803952}{923521} a^{3} + \frac{9909977575470350951831216400}{923521} a^{2} - \frac{5978197446809240162656682401}{923521} a - \frac{1713525152117869864310632982}{923521} \)
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 5 a^{3} - 75 a^{2} + 320 a - 384\) , \( 330 a^{3} - 1847 a^{2} + 3763 a - 2740\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a^{3}-75a^{2}+320a-384\right){x}+330a^{3}-1847a^{2}+3763a-2740$
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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.