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
31.4-a5 31.4-a $6$
$8$
\(\Q(\zeta_{15})^+\) $4$
$[4, 0]$
31.4
\( 31 \)
\( 31^{2} \)
$4.60400$
$(2a^3-8a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2 \)
$1$
$226.2402485$
0.843147624
\( \frac{2900297}{961} a^{3} + \frac{1134908}{961} a^{2} - \frac{10585572}{961} a - \frac{2345377}{961} \)
\( \bigl[a^{2} - 1\) , \( -a^{3} + 3 a - 1\) , \( a^{3} - 2 a\) , \( -a^{3} + a^{2} + a - 2\) , \( -a^{3} + a^{2} + 4 a - 6\bigr] \) ${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{3}+3a-1\right){x}^{2}+\left(-a^{3}+a^{2}+a-2\right){x}-a^{3}+a^{2}+4a-6$
31.4-b3 31.4-b $6$
$8$
\(\Q(\zeta_{15})^+\) $4$
$[4, 0]$
31.4
\( 31 \)
\( 31^{2} \)
$4.60400$
$(2a^3-8a+1)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2 \)
$1$
$757.6135842$
0.705864781
\( \frac{2900297}{961} a^{3} + \frac{1134908}{961} a^{2} - \frac{10585572}{961} a - \frac{2345377}{961} \)
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+{x}$
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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.
