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
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
23.2
\( 23 \)
\( 23^{2} \)
$0.95869$
$(2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$20.77155964$
2.119988428
\( -\frac{1596672}{529} a + \frac{6322752}{529} \)
\( \bigl[a\) , \( -a\) , \( 1\) , \( -12 a - 23\) , \( -20 a - 47\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-12a-23\right){x}-20a-47$
23.2-a2
23.2-a
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
23.2
\( 23 \)
\( -23 \)
$0.95869$
$(2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 1 \)
$1$
$10.38577982$
2.119988428
\( \frac{66417408}{23} a + \frac{162689472}{23} \)
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -2 a - 1\) , \( -a - 1\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-2a-1\right){x}-a-1$
23.2-b1
23.2-b
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
23.2
\( 23 \)
\( 23^{2} \)
$0.95869$
$(2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.078486626$
$42.58064027$
0.682185096
\( -\frac{1596672}{529} a + \frac{6322752}{529} \)
\( \bigl[a\) , \( -a\) , \( 1\) , \( -a + 1\) , \( 0\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-a+1\right){x}$
23.2-b2
23.2-b
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
23.2
\( 23 \)
\( -23 \)
$0.95869$
$(2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$0.156973252$
$42.58064027$
0.682185096
\( \frac{66417408}{23} a + \frac{162689472}{23} \)
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -11 a + 23\) , \( -198 a + 482\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-11a+23\right){x}-198a+482$
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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.