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
20412.2-d2
20412.2-d
$3$
$9$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
20412.2
\( 2^{2} \cdot 3^{6} \cdot 7 \)
\( 2^{6} \cdot 3^{6} \cdot 7^{6} \)
$2.82591$
$(a), (-a+1), (-2a+1), (3)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3Cs.1.1
$1$
\( 2 \cdot 3 \)
$1.272828819$
$2.035709838$
2.611593553
\( -\frac{7414875}{2744} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -12\) , \( 24\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-12{x}+24$
20412.2-w2
20412.2-w
$3$
$9$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
20412.2
\( 2^{2} \cdot 3^{6} \cdot 7 \)
\( 2^{6} \cdot 3^{18} \cdot 7^{6} \)
$2.82591$
$(a), (-a+1), (-2a+1), (3)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3Cs.1.1
$1$
\( 2 \cdot 3^{4} \)
$0.539536617$
$0.678569946$
9.963203988
\( -\frac{7414875}{2744} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -110\) , \( -539\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-110{x}-539$
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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.