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
19.3-a1
19.3-a
$2$
$3$
3.3.1489.1
$3$
$[3, 0]$
19.3
\( 19 \)
\( 19^{3} \)
$5.63263$
$(a-3)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$9$
\( 3 \)
$1$
$35.62197492$
2.769439609
\( -\frac{5575931}{6859} a^{2} + \frac{11039397}{6859} a + \frac{24746668}{6859} \)
\( \bigl[a\) , \( -a^{2} + a + 6\) , \( a^{2} - 2 a - 6\) , \( -3 a^{2} + 8 a + 13\) , \( -6 a^{2} + 19 a + 18\bigr] \)
${y}^2+a{x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-3a^{2}+8a+13\right){x}-6a^{2}+19a+18$
19.3-c2
19.3-c
$2$
$3$
3.3.1489.1
$3$
$[3, 0]$
19.3
\( 19 \)
\( 19^{3} \)
$5.63263$
$(a-3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$0.519040349$
$91.56975355$
3.695107449
\( -\frac{5575931}{6859} a^{2} + \frac{11039397}{6859} a + \frac{24746668}{6859} \)
\( \bigl[a + 1\) , \( a^{2} - a - 7\) , \( 1\) , \( 6 a + 13\) , \( 2 a^{2} + 4 a - 1\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(6a+13\right){x}+2a^{2}+4a-1$
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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.