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
338.1-h3
338.1-h
$3$
$9$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
338.1
\( 2 \cdot 13^{2} \)
\( 2^{2} \cdot 13^{2} \)
$2.02743$
$(a+3), (13)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.1
$1$
\( 2 \)
$1.688060403$
$21.53136195$
3.052797172
\( \frac{12167}{26} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}$
338.1-k3
338.1-k
$3$
$9$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
338.1
\( 2 \cdot 13^{2} \)
\( 2^{2} \cdot 13^{2} \)
$2.02743$
$(a+3), (13)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B
$1$
\( 2 \)
$0.166288191$
$12.10583107$
1.521727872
\( \frac{12167}{26} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( 3\) , \( 1\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+3{x}+1$
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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.