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
361.1-a2
361.1-a
$3$
$9$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
361.1
\( 19^{2} \)
\( 19^{6} \)
$0.77901$
$(19)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3Cs.1.1
$1$
\( 3 \)
$1$
$2.805927025$
0.935309008
\( -\frac{89915392}{6859} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -9\) , \( -15\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}-9{x}-15$
29241.1-b2
29241.1-b
$3$
$9$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
29241.1
\( 3^{4} \cdot 19^{2} \)
\( 3^{12} \cdot 19^{6} \)
$2.33704$
$(3), (19)$
$2$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3Cs.1.1
$1$
\( 2^{2} \cdot 3 \)
$0.622939939$
$0.935309008$
3.107420464
\( -\frac{89915392}{6859} \)
\( \bigl[0\) , \( 0\) , \( i\) , \( -84\) , \( -315\bigr] \)
${y}^2+i{y}={x}^{3}-84{x}-315$
92416.1-b2
92416.1-b
$3$
$9$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
92416.1
\( 2^{8} \cdot 19^{2} \)
\( 2^{12} \cdot 19^{6} \)
$3.11606$
$(a+1), (19)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3Cs
$1$
\( 2 \cdot 3 \)
$0.151745901$
$1.402963512$
5.109455107
\( -\frac{89915392}{6859} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -37\) , \( -81\bigr] \)
${y}^2={x}^{3}-{x}^{2}-37{x}-81$
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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.