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
1521.3-CMb1
1521.3-CMb
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1521.3
\( 3^{2} \cdot 13^{2} \)
\( 3^{6} \cdot 13^{10} \)
$0.96657$
$(-2a+1), (4a-3)$
0
$\mathsf{trivial}$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$13$
13Cs.5.1
$1$
\( 1 \)
$1$
$0.956447781$
1.104410767
\( 0 \)
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( 135 a + 29\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+135a+29$
1521.3-CMa1
1521.3-CMa
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1521.3
\( 3^{2} \cdot 13^{2} \)
\( 3^{6} \cdot 13^{4} \)
$0.96657$
$(-2a+1), (4a-3)$
0
$\Z/3\Z$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$3, 13$
3B.1.1[2] , 13Cs.5.1
$1$
\( 3 \)
$1$
$3.448521516$
1.327336550
\( 0 \)
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( 3 a - 2\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+3a-2$
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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.