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-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-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
\( \frac{1596672}{529} a + \frac{6322752}{529} \)
\( \bigl[a\) , \( a\) , \( 1\) , \( 1\) , \( 0\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+{x}$
368.1-d2
368.1-d
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
368.1
\( 2^{4} \cdot 23 \)
\( 2^{12} \cdot 23^{2} \)
$1.91737$
$(-a+2), (-2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$0.761421448$
$21.29032013$
3.309037413
\( \frac{1596672}{529} a + \frac{6322752}{529} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( -2 a - 5\) , \( 5 a + 12\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(-2a-5\right){x}+5a+12$
368.1-f2
368.1-f
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
368.1
\( 2^{4} \cdot 23 \)
\( 2^{12} \cdot 23^{2} \)
$1.91737$
$(-a+2), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$10.38577982$
1.059994214
\( \frac{1596672}{529} a + \frac{6322752}{529} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 42 a - 101\) , \( 217 a - 532\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(42a-101\right){x}+217a-532$
529.2-b2
529.2-b
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
529.2
\( 23^{2} \)
\( 23^{8} \)
$2.09946$
$(-2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$2.857820611$
$5.674868404$
6.620871118
\( \frac{1596672}{529} a + \frac{6322752}{529} \)
\( \bigl[a\) , \( -a\) , \( 1\) , \( 364 a - 893\) , \( -4212 a + 10317\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(364a-893\right){x}-4212a+10317$
529.2-f2
529.2-f
$2$
$2$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
529.2
\( 23^{2} \)
\( 23^{8} \)
$2.09946$
$(-2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.451343381$
$6.776378617$
1.248616635
\( \frac{1596672}{529} a + \frac{6322752}{529} \)
\( \bigl[a\) , \( -a\) , \( 1\) , \( -7 a - 29\) , \( 35 a + 40\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-7a-29\right){x}+35a+40$
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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.