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
31.3-a6
31.3-a
$6$
$8$
\(\Q(\zeta_{15})^+\)
$4$
$[4, 0]$
31.3
\( 31 \)
\( 31^{16} \)
$4.60400$
$(-2a^3-2a^2+6a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 2 \)
$1$
$14.14001553$
0.843147624
\( \frac{17216766333469942774436560624}{727423121747185263828481} a^{3} - \frac{52426907107682729263745202448}{727423121747185263828481} a^{2} + \frac{33240480633127353737657993249}{727423121747185263828481} a + \frac{9399400109123561576571971302}{727423121747185263828481} \)
\( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -175 a^{3} - 61 a^{2} + 638 a + 137\) , \( 89 a^{3} + 13 a^{2} - 402 a - 82\bigr] \)
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(-175a^{3}-61a^{2}+638a+137\right){x}+89a^{3}+13a^{2}-402a-82$
31.3-b6
31.3-b
$6$
$8$
\(\Q(\zeta_{15})^+\)
$4$
$[4, 0]$
31.3
\( 31 \)
\( 31^{16} \)
$4.60400$
$(-2a^3-2a^2+6a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$16$
\( 2 \)
$1$
$2.959428063$
0.705864781
\( \frac{17216766333469942774436560624}{727423121747185263828481} a^{3} - \frac{52426907107682729263745202448}{727423121747185263828481} a^{2} + \frac{33240480633127353737657993249}{727423121747185263828481} a + \frac{9399400109123561576571971302}{727423121747185263828481} \)
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -5 a^{3} - 15 a^{2} + 40 a + 16\) , \( -8 a^{3} + a^{2} + 125 a - 166\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a^{3}-15a^{2}+40a+16\right){x}-8a^{3}+a^{2}+125a-166$
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Pari/GP
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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.