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
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
23.1
\( 23 \)
\( -23 \)
$0.95869$
$(-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 1 \)
$1$
$10.38577982$
2.119988428
\( -\frac{66417408}{23} a + \frac{162689472}{23} \)
\( \bigl[a\) , \( a\) , \( a + 1\) , \( a - 1\) , \( -1\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(a-1\right){x}-1$
23.1-a2
23.1-a
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
23.1
\( 23 \)
\( 23^{2} \)
$0.95869$
$(-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$20.77155964$
2.119988428
\( \frac{1596672}{529} a + \frac{6322752}{529} \)
\( \bigl[a\) , \( a\) , \( 1\) , \( 11 a - 23\) , \( 20 a - 47\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(11a-23\right){x}+20a-47$
23.1-b1
23.1-b
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
23.1
\( 23 \)
\( -23 \)
$0.95869$
$(-2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$0.156973252$
$42.58064027$
0.682185096
\( -\frac{66417408}{23} a + \frac{162689472}{23} \)
\( \bigl[a\) , \( a\) , \( a + 1\) , \( 10 a + 23\) , \( 197 a + 482\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(10a+23\right){x}+197a+482$
23.1-b2
23.1-b
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
23.1
\( 23 \)
\( 23^{2} \)
$0.95869$
$(-2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.078486626$
$42.58064027$
0.682185096
\( \frac{1596672}{529} a + \frac{6322752}{529} \)
\( \bigl[a\) , \( a\) , \( 1\) , \( 1\) , \( 0\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+{x}$
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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.