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
722.1-a3
722.1-a
$3$
$9$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
722.1
\( 2 \cdot 19^{2} \)
\( 2^{18} \cdot 19^{6} \)
$0.92641$
$(a+1), (19)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3Cs.1.1
$1$
\( 2 \cdot 3 \)
$1$
$1.136863399$
0.757908933
\( \frac{94196375}{3511808} \)
\( \bigl[i\) , \( 0\) , \( i\) , \( 10\) , \( -90\bigr] \)
${y}^2+i{x}{y}+i{y}={x}^{3}+10{x}-90$
58482.1-f3
58482.1-f
$3$
$9$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
58482.1
\( 2 \cdot 3^{4} \cdot 19^{2} \)
\( 2^{18} \cdot 3^{12} \cdot 19^{6} \)
$2.77923$
$(a+1), (3), (19)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3Cs.1.1
$1$
\( 2 \cdot 3^{3} \)
$1.513162762$
$0.378954466$
6.881037449
\( \frac{94196375}{3511808} \)
\( \bigl[i\) , \( 1\) , \( i\) , \( 86\) , \( 2437\bigr] \)
${y}^2+i{x}{y}+i{y}={x}^{3}+{x}^{2}+86{x}+2437$
92416.1-d3
92416.1-d
$3$
$9$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
92416.1
\( 2^{8} \cdot 19^{2} \)
\( 2^{42} \cdot 19^{6} \)
$3.11606$
$(a+1), (19)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3Cs
$1$
\( 2^{2} \cdot 3 \)
$0.472595983$
$0.284215849$
6.447324923
\( \frac{94196375}{3511808} \)
\( \bigl[0\) , \( -i\) , \( 0\) , \( -152\) , \( 5776 i\bigr] \)
${y}^2={x}^{3}-i{x}^{2}-152{x}+5776i$
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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.