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
31.2-a1
31.2-a
$1$
$1$
6.6.966125.1
$6$
$[6, 0]$
31.2
\( 31 \)
\( -31 \)
$116.93253$
$(a^2-2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$2487.229488$
2.53046
\( \frac{188987486}{31} a^{5} - \frac{272082083}{31} a^{4} - \frac{1014613018}{31} a^{3} + \frac{1202373611}{31} a^{2} + \frac{985030371}{31} a - \frac{434306805}{31} \)
\( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 9 a^{2} + 4 a - 2\) , \( 2 a^{5} - 3 a^{4} - 10 a^{3} + 13 a^{2} + 8 a - 2\) , \( a^{5} - a^{4} - 4 a^{3} + 5 a^{2} - 3\) , \( 11 a^{5} - 7 a^{4} - 46 a^{3} + 33 a^{2} + 12 a - 5\) , \( 16 a^{5} - 6 a^{4} - 64 a^{3} + 34 a^{2} + 12 a - 7\bigr] \)
${y}^2+\left(2a^{5}-2a^{4}-9a^{3}+9a^{2}+4a-2\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+5a^{2}-3\right){y}={x}^{3}+\left(2a^{5}-3a^{4}-10a^{3}+13a^{2}+8a-2\right){x}^{2}+\left(11a^{5}-7a^{4}-46a^{3}+33a^{2}+12a-5\right){x}+16a^{5}-6a^{4}-64a^{3}+34a^{2}+12a-7$
31.2-b1
31.2-b
$1$
$1$
6.6.966125.1
$6$
$[6, 0]$
31.2
\( 31 \)
\( -31 \)
$116.93253$
$(a^2-2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$0.005963385$
$59064.27455$
2.15007
\( \frac{188987486}{31} a^{5} - \frac{272082083}{31} a^{4} - \frac{1014613018}{31} a^{3} + \frac{1202373611}{31} a^{2} + \frac{985030371}{31} a - \frac{434306805}{31} \)
\( \bigl[a^{5} - 5 a^{3} + 4 a + 1\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 9 a^{2} + 11 a - 2\) , \( a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 5 a - 2\) , \( -a^{5} + 3 a^{4} + 6 a^{3} - 12 a^{2} - 7 a + 5\) , \( 3 a^{5} - a^{4} - 14 a^{3} + 6 a^{2} + 9 a - 3\bigr] \)
${y}^2+\left(a^{5}-5a^{3}+4a+1\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+5a^{2}+5a-2\right){y}={x}^{3}+\left(2a^{5}-2a^{4}-11a^{3}+9a^{2}+11a-2\right){x}^{2}+\left(-a^{5}+3a^{4}+6a^{3}-12a^{2}-7a+5\right){x}+3a^{5}-a^{4}-14a^{3}+6a^{2}+9a-3$
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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.