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-a1
19.1-a
$2$
$2$
3.3.316.1
$3$
$[3, 0]$
19.1
\( 19 \)
\( -19 \)
$2.59482$
$(-a^2+a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$0.141881150$
$147.0278174$
0.880120090
\( -\frac{613}{19} a^{2} + \frac{19934}{19} a + \frac{42110}{19} \)
\( \bigl[a\) , \( -1\) , \( 1\) , \( -2 a + 1\) , \( -a^{2} + 2 a - 1\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-2a+1\right){x}-a^{2}+2a-1$
19.1-a2
19.1-a
$2$
$2$
3.3.316.1
$3$
$[3, 0]$
19.1
\( 19 \)
\( - 19^{2} \)
$2.59482$
$(-a^2+a-1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.070940575$
$147.0278174$
0.880120090
\( -\frac{2773405}{361} a^{2} + \frac{775470}{361} a + \frac{13611342}{361} \)
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 2 a - 1\) , \( a - 1\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a-1\right){x}+a-1$
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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.