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
38.1-a2
38.1-a
$3$
$9$
\(\Q(\sqrt{19}) \)
$2$
$[2, 0]$
38.1
\( 2 \cdot 19 \)
\( 2^{54} \cdot 19^{2} \)
$1.93415$
$(-3a+13), (a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.2
$1$
\( 2^{2} \)
$8.273244123$
$0.397165580$
3.015300745
\( -\frac{69173457625}{2550136832} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -86\) , \( -2456\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-86{x}-2456$
38.1-d2
38.1-d
$3$
$9$
\(\Q(\sqrt{19}) \)
$2$
$[2, 0]$
38.1
\( 2 \cdot 19 \)
\( 2^{54} \cdot 19^{2} \)
$1.93415$
$(-3a+13), (a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B
$1$
\( 2^{2} \cdot 3^{3} \)
$0.086075062$
$1.446313524$
3.084514027
\( -\frac{69173457625}{2550136832} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( -84\) , \( 2287\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-84{x}+2287$
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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.