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
19.1-a3
19.1-a
$3$
$9$
3.3.361.1
$3$
$[3, 0]$
19.1
\( 19 \)
\( - 19^{3} \)
$2.77343$
$(a^2-a-4)$
0
$\Z/9\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.1
$9$
\( 3 \)
$1$
$67.88132220$
1.190900389
\( \frac{32768}{19} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( 0\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}+{x}$
361.1-b1
361.1-b
$3$
$9$
3.3.361.1
$3$
$[3, 0]$
361.1
\( 19^{2} \)
\( - 19^{9} \)
$4.53047$
$(a^2-a-4)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B
$1$
\( 2 \)
$1$
$16.12708123$
1.697587498
\( \frac{32768}{19} \)
\( \bigl[0\) , \( -a - 1\) , \( a^{2} - 3\) , \( 37 a^{2} + 48 a - 111\) , \( -32 a^{2} - 41 a + 96\bigr] \)
${y}^2+\left(a^{2}-3\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(37a^{2}+48a-111\right){x}-32a^{2}-41a+96$
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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.