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
361.2-a1
361.2-a
$3$
$9$
\(\Q(\sqrt{-67}) \)
$2$
$[0, 1]$
361.2
\( 19^{2} \)
\( 19^{2} \)
$3.18825$
$(a+1), (a-2)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.2
$1$
\( 1 \)
$5.618953292$
$0.935309008$
2.568225355
\( -\frac{50357871050752}{19} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -769\) , \( -8470\bigr] \)
${y}^2+{y}={x}^3+{x}^2-769{x}-8470$
361.2-a2
361.2-a
$3$
$9$
\(\Q(\sqrt{-67}) \)
$2$
$[0, 1]$
361.2
\( 19^{2} \)
\( 19^{6} \)
$3.18825$
$(a+1), (a-2)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3Cs.1.1
$1$
\( 3^{2} \)
$1.872984430$
$2.805927025$
2.568225355
\( -\frac{89915392}{6859} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -9\) , \( -15\bigr] \)
${y}^2+{y}={x}^3+{x}^2-9{x}-15$
361.2-a3
361.2-a
$3$
$9$
\(\Q(\sqrt{-67}) \)
$2$
$[0, 1]$
361.2
\( 19^{2} \)
\( 19^{2} \)
$3.18825$
$(a+1), (a-2)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.1
$1$
\( 1 \)
$5.618953292$
$8.417781075$
2.568225355
\( \frac{32768}{19} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( 0\bigr] \)
${y}^2+{y}={x}^3+{x}^2+{x}$
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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.