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
23.2-a1
23.2-a
$2$
$2$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
23.2
\( 23 \)
\( - 23^{2} \)
$0.70557$
$(3a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$6.496490929$
0.900901198
\( -\frac{50955500525}{529} a + \frac{117339251834}{529} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 8 a - 7\) , \( 10 a - 14\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(8a-7\right){x}+10a-14$
23.2-a2
23.2-a
$2$
$2$
\(\Q(\sqrt{13}) \)
$2$
$[2, 0]$
23.2
\( 23 \)
\( -23 \)
$0.70557$
$(3a-4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1$
$12.99298185$
0.900901198
\( \frac{156803}{23} a - \frac{207479}{23} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 3 a + 3\) , \( 2 a + 2\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a+3\right){x}+2a+2$
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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.