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
15376.1-CMb1
15376.1-CMb
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
15376.1
\( 2^{4} \cdot 31^{2} \)
\( 2^{16} \cdot 31^{2} \)
$1.72349$
$(-6a+1), (2)$
0
$\mathsf{trivial}$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$31$
31Cs.7.1
$1$
\( 1 \)
$1$
$3.144665154$
3.631146547
\( 0 \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a\) , \( 2 a - 5\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+a{x}+2a-5$
15376.1-CMa1
15376.1-CMa
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
15376.1
\( 2^{4} \cdot 31^{2} \)
\( 2^{8} \cdot 31^{6} \)
$1.72349$
$(-6a+1), (2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$2, 31$
2Cs , 31Cs.7.1
$1$
\( 2^{2} \)
$1$
$1.589060775$
0.458722333
\( 0 \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a\) , \( -34 a + 32\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+a{x}-34a+32$
15376.1-CMa2
15376.1-CMa
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
15376.1
\( 2^{4} \cdot 31^{2} \)
\( 2^{16} \cdot 31^{6} \)
$1.72349$
$(-6a+1), (2)$
0
$\Z/2\Z$
$\textsf{yes}$
$-12$
$\mathrm{U}(1)$
✓
✓
$31$
31Cs.7.1
$1$
\( 2 \)
$1$
$0.794530387$
0.458722333
\( 54000 \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 121 a - 175\) , \( -731 a + 608\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(121a-175\right){x}-731a+608$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.