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
32.4-a1
32.4-a
$1$
$1$
\(\Q(\sqrt{-31}) \)
$2$
$[0, 1]$
32.4
\( 2^{5} \)
\( 2^{20} \)
$1.18333$
$(2,a), (2,a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2Cn , 5S4
$1$
\( 2 \)
$0.139158379$
$8.191609121$
1.637901283
\( -1536 a + 2816 \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( a + 2\) , \( -3\bigr] \)
${y}^2={x}^3-{x}^2+\left(a+2\right){x}-3$
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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.