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
31744.2-a1
31744.2-a
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
31744.2
\( 2^{10} \cdot 31 \)
\( 2^{18} \cdot 31 \)
$2.06593$
$(6a-5), (2)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{2} \)
$0.037717178$
$3.634581107$
2.532695138
\( \frac{34992}{31} a - \frac{5832}{31} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2 a + 3\) , \( -a - 3\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a+3\right){x}-a-3$
31744.2-b1
31744.2-b
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
31744.2
\( 2^{10} \cdot 31 \)
\( 2^{18} \cdot 31 \)
$2.06593$
$(6a-5), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2 \)
$0.164986794$
$3.552150997$
2.706885987
\( \frac{53240}{31} a - \frac{63888}{31} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( 4 a - 4\) , \( 4 a - 4\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(4a-4\right){x}+4a-4$
31744.2-c1
31744.2-c
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
31744.2
\( 2^{10} \cdot 31 \)
\( 2^{18} \cdot 31 \)
$2.06593$
$(6a-5), (2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2 \)
$0.219026084$
$3.552150997$
3.593491459
\( \frac{53240}{31} a - \frac{63888}{31} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 4 a - 4\) , \( -4 a + 4\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(4a-4\right){x}-4a+4$
31744.2-d1
31744.2-d
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
31744.2
\( 2^{10} \cdot 31 \)
\( 2^{18} \cdot 31 \)
$2.06593$
$(6a-5), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 1 \)
$1$
$3.634581107$
4.196852761
\( \frac{34992}{31} a - \frac{5832}{31} \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 3\) , \( a\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a-3\right){x}+a$
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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.