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
1083.2-b1
1083.2-b
$6$
$8$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1083.2
\( 3 \cdot 19^{2} \)
\( 3 \cdot 19^{10} \)
$0.88788$
$(-2a+1), (-5a+3), (-5a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$0.816172249$
0.942434535
\( -\frac{7240152655469734}{50950689123} a + \frac{1727319988870667}{50950689123} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( 130 a + 63\) , \( -464 a + 999\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(130a+63\right){x}-464a+999$
61731.2-b5
61731.2-b
$6$
$8$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
61731.2
\( 3^{2} \cdot 19^{3} \)
\( 3^{7} \cdot 19^{16} \)
$2.43964$
$(-2a+1), (-5a+3), (-5a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{5} \)
$1$
$0.108104655$
0.998628029
\( -\frac{7240152655469734}{50950689123} a + \frac{1727319988870667}{50950689123} \)
\( \bigl[1\) , \( a\) , \( a + 1\) , \( 1097 a - 10240\) , \( -68165 a + 397614\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(1097a-10240\right){x}-68165a+397614$
61731.3-b5
61731.3-b
$6$
$8$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
61731.3
\( 3^{2} \cdot 19^{3} \)
\( 3^{7} \cdot 19^{16} \)
$2.43964$
$(-2a+1), (-5a+3), (-5a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{5} \)
$1$
$0.108104655$
0.998628029
\( -\frac{7240152655469734}{50950689123} a + \frac{1727319988870667}{50950689123} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 5287 a + 5950\) , \( -322106 a + 404732\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5287a+5950\right){x}-322106a+404732$
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Pari/GP
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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.