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-a1
31.1-a
$6$
$8$
\(\Q(\zeta_{15})^+\)
$4$
$[4, 0]$
31.1
\( 31 \)
\( 31^{4} \)
$4.60400$
$(a^3+2a^2-3a-3)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$226.2402485$
0.843147624
\( \frac{13262138608154212980818020352}{923521} a^{3} - \frac{16034680544860826249617094257}{923521} a^{2} - \frac{49696393399932989894285277456}{923521} a + \frac{63437929696698697519404008684}{923521} \)
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 1\) , \( -427 a^{3} - 156 a^{2} + 1210 a - 328\) , \( 5301 a^{3} + 2573 a^{2} - 14446 a + 2048\bigr] \)
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+{y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(-427a^{3}-156a^{2}+1210a-328\right){x}+5301a^{3}+2573a^{2}-14446a+2048$
31.1-b1
31.1-b
$6$
$8$
\(\Q(\zeta_{15})^+\)
$4$
$[4, 0]$
31.1
\( 31 \)
\( 31^{4} \)
$4.60400$
$(a^3+2a^2-3a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$16$
\( 2 \)
$1$
$2.959428063$
0.705864781
\( \frac{13262138608154212980818020352}{923521} a^{3} - \frac{16034680544860826249617094257}{923521} a^{2} - \frac{49696393399932989894285277456}{923521} a + \frac{63437929696698697519404008684}{923521} \)
\( \bigl[a^{2} - 2\) , \( -a^{2} + 1\) , \( 0\) , \( -80 a^{3} + 335 a^{2} + 315 a - 1284\) , \( -2177 a^{3} + 4753 a^{2} + 8378 a - 18117\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(-a^{2}+1\right){x}^{2}+\left(-80a^{3}+335a^{2}+315a-1284\right){x}-2177a^{3}+4753a^{2}+8378a-18117$
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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.