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
5776.3-CMc1
5776.3-CMc
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
5776.3
\( 2^{4} \cdot 19^{2} \)
\( 2^{8} \cdot 19^{10} \)
$1.34929$
$(-5a+2), (2)$
0
$\mathsf{trivial}$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$19$
19Cs.4.1
$1$
\( 3 \)
$1$
$0.760664859$
2.635020368
\( 0 \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( 349 a - 159\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}+349a-159$
5776.3-CMb1
5776.3-CMb
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
5776.3
\( 2^{4} \cdot 19^{2} \)
\( 2^{8} \cdot 19^{6} \)
$1.34929$
$(-5a+2), (2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$2, 19$
2Cs , 19Cs.4.1
$1$
\( 2^{2} \cdot 3 \)
$1$
$2.029759365$
1.757823174
\( 0 \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( 6 a - 18\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}+6a-18$
5776.3-CMb2
5776.3-CMb
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
5776.3
\( 2^{4} \cdot 19^{2} \)
\( 2^{16} \cdot 19^{6} \)
$1.34929$
$(-5a+2), (2)$
0
$\Z/2\Z$
$\textsf{yes}$
$-12$
$\mathrm{U}(1)$
✓
✓
$19$
19Cs.4.1
$1$
\( 2 \cdot 3 \)
$1$
$1.014879682$
1.757823174
\( 54000 \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -104 a + 80\) , \( 180 a - 460\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-104a+80\right){x}+180a-460$
5776.3-CMa1
5776.3-CMa
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
5776.3
\( 2^{4} \cdot 19^{2} \)
\( 2^{8} \cdot 19^{2} \)
$1.34929$
$(-5a+2), (2)$
$2$
$\mathsf{trivial}$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$19$
19Cs.4.1
$1$
\( 3 \)
$0.018683933$
$5.416213237$
1.402215272
\( 0 \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( -a\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-a$
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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.