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
324.1-a1
324.1-a
$2$
$3$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
324.1
\( 2^{2} \cdot 3^{4} \)
\( 2^{4} \cdot 3^{6} \)
$1.31330$
$(a+1), (a)$
$1$
$\mathsf{trivial}$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
✓
$3$
3B.1.2
$1$
\( 1 \)
$0.450320685$
$7.431447726$
1.932122672
\( 0 \)
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -8 a - 14\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}-8a-14$
324.1-a2
324.1-a
$2$
$3$
\(\Q(\sqrt{3}) \)
$2$
$[2, 0]$
324.1
\( 2^{2} \cdot 3^{4} \)
\( 2^{4} \cdot 3^{6} \)
$1.31330$
$(a+1), (a)$
$1$
$\Z/3\Z$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
✓
$3$
3B.1.1
$1$
\( 3^{2} \)
$0.150106895$
$22.29434318$
1.932122672
\( 0 \)
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( 7 a + 12\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+7a+12$
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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.