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
23.1-a1
23.1-a
$1$
$1$
3.3.697.1
$3$
$[3, 0]$
23.1
\( 23 \)
\( 23 \)
$3.97841$
$(a^2-3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$0.209680137$
$110.8131942$
2.640302162
\( -\frac{212670}{23} a^{2} + \frac{478001}{23} a + \frac{480840}{23} \)
\( \bigl[a^{2} - a - 4\) , \( a^{2} - 4\) , \( a + 1\) , \( a + 2\) , \( -a^{2} + 2 a + 2\bigr] \)
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(a+2\right){x}-a^{2}+2a+2$
23.1-b1
23.1-b
$1$
$1$
3.3.697.1
$3$
$[3, 0]$
23.1
\( 23 \)
\( 23 \)
$3.97841$
$(a^2-3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$49.26387972$
1.866002504
\( -\frac{212670}{23} a^{2} + \frac{478001}{23} a + \frac{480840}{23} \)
\( \bigl[a\) , \( a^{2} - a - 6\) , \( a^{2} - 5\) , \( -3 a^{2} - 6 a + 2\) , \( a^{2} - 3 a - 11\bigr] \)
${y}^2+a{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-3a^{2}-6a+2\right){x}+a^{2}-3a-11$
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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.