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-b1
19.1-b
$2$
$2$
4.4.8069.1
$4$
$[4, 0]$
19.1
\( 19 \)
\( 19^{2} \)
$11.59825$
$(a^2+a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$402.9403342$
2.242853406
\( \frac{921050783480}{361} a^{3} + \frac{1052547388417}{361} a^{2} - \frac{2349627001920}{361} a - \frac{429808776872}{361} \)
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a - 1\) , \( a\) , \( -11 a^{2} - 8 a + 29\) , \( -14 a^{3} - 5 a^{2} + 45 a - 22\bigr] \)
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-11a^{2}-8a+29\right){x}-14a^{3}-5a^{2}+45a-22$
19.1-e2
19.1-e
$2$
$2$
4.4.8069.1
$4$
$[4, 0]$
19.1
\( 19 \)
\( 19^{2} \)
$11.59825$
$(a^2+a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$99.74404697$
0.555197026
\( \frac{921050783480}{361} a^{3} + \frac{1052547388417}{361} a^{2} - \frac{2349627001920}{361} a - \frac{429808776872}{361} \)
\( \bigl[a^{2} - 3\) , \( -a^{3} + 5 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} - 8 a^{2} - 3 a + 21\) , \( -5 a^{3} - 12 a^{2} + 7 a + 20\bigr] \)
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(-a^{3}+5a-1\right){x}^{2}+\left(-a^{3}-8a^{2}-3a+21\right){x}-5a^{3}-12a^{2}+7a+20$
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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.