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-d3
20412.2-d
$3$
$9$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
20412.2
\( 2^{2} \cdot 3^{6} \cdot 7 \)
\( 2^{18} \cdot 3^{18} \cdot 7^{2} \)
$2.82591$
$(a), (-a+1), (-2a+1), (3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.2
$1$
\( 2 \cdot 3 \)
$0.424276273$
$0.678569946$
2.611593553
\( \frac{4492125}{3584} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 93\) , \( -235\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+93{x}-235$
20412.2-w3
20412.2-w
$3$
$9$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
20412.2
\( 2^{2} \cdot 3^{6} \cdot 7 \)
\( 2^{18} \cdot 3^{6} \cdot 7^{2} \)
$2.82591$
$(a), (-a+1), (-2a+1), (3)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1
$1$
\( 2 \cdot 3^{4} \)
$0.179845539$
$2.035709838$
9.963203988
\( \frac{4492125}{3584} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 10\) , \( 5\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+10{x}+5$
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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.