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-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
\( -\frac{1596672}{529} a + \frac{6322752}{529} \)
\( \bigl[a\) , \( -a\) , \( 1\) , \( -a + 1\) , \( 0\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-a+1\right){x}$
368.2-d1
368.2-d
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
368.2
\( 2^{4} \cdot 23 \)
\( 2^{12} \cdot 23^{2} \)
$1.91737$
$(-a+2), (2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$0.761421448$
$21.29032013$
3.309037413
\( -\frac{1596672}{529} a + \frac{6322752}{529} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( 2 a - 5\) , \( -5 a + 12\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(2a-5\right){x}-5a+12$
368.2-f1
368.2-f
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
368.2
\( 2^{4} \cdot 23 \)
\( 2^{12} \cdot 23^{2} \)
$1.91737$
$(-a+2), (2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$10.38577982$
1.059994214
\( -\frac{1596672}{529} a + \frac{6322752}{529} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -42 a - 101\) , \( -217 a - 532\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(-42a-101\right){x}-217a-532$
529.3-b1
529.3-b
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
529.3
\( 23^{2} \)
\( 23^{8} \)
$2.09946$
$(2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$2.857820611$
$5.674868404$
6.620871118
\( -\frac{1596672}{529} a + \frac{6322752}{529} \)
\( \bigl[a\) , \( a\) , \( 1\) , \( -365 a - 893\) , \( 4212 a + 10317\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-365a-893\right){x}+4212a+10317$
529.3-f1
529.3-f
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
529.3
\( 23^{2} \)
\( 23^{8} \)
$2.09946$
$(2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.451343381$
$6.776378617$
1.248616635
\( -\frac{1596672}{529} a + \frac{6322752}{529} \)
\( \bigl[a\) , \( a\) , \( 1\) , \( 6 a - 29\) , \( -35 a + 40\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(6a-29\right){x}-35a+40$
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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.