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-a6 31.1-a $6$
$8$
\(\Q(\zeta_{15})^+\) $4$
$[4, 0]$
31.1
\( 31 \)
\( 31^{2} \)
$4.60400$
$(a^3+2a^2-3a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $4$
\( 2 \)
$1$
$14.14001553$
0.843147624
\( -\frac{236284316384699073}{961} a^{3} + \frac{698632890478410244}{961} a^{2} - \frac{421506652954098940}{961} a - \frac{120811375486877791}{961} \)
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 1\) , \( -327 a^{3} - 341 a^{2} + 895 a + 197\) , \( -4716 a^{3} - 4369 a^{2} + 12267 a + 2711\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+{y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(-327a^{3}-341a^{2}+895a+197\right){x}-4716a^{3}-4369a^{2}+12267a+2711$
31.1-b4 31.1-b $6$
$8$
\(\Q(\zeta_{15})^+\) $4$
$[4, 0]$
31.1
\( 31 \)
\( 31^{2} \)
$4.60400$
$(a^3+2a^2-3a-3)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2 \)
$1$
$757.6135842$
0.705864781
\( -\frac{236284316384699073}{961} a^{3} + \frac{698632890478410244}{961} a^{2} - \frac{421506652954098940}{961} a - \frac{120811375486877791}{961} \)
\( \bigl[a^{2} - 2\) , \( -a^{2} + 1\) , \( 0\) , \( 5 a^{3} - 20 a^{2} - 20 a - 9\) , \( -4 a^{3} + 99 a^{2} + 23 a - 5\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(-a^{2}+1\right){x}^{2}+\left(5a^{3}-20a^{2}-20a-9\right){x}-4a^{3}+99a^{2}+23a-5$
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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.
