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
$2$
$2$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
23.2
\( 23 \)
\( 23^{2} \)
$1.71718$
$(a-7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.664676963$
$38.88510373$
2.945428784
\( -\frac{41151093}{529} a - \frac{160022908}{529} \)
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( a - 3\) , \( -12 a + 51\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-3\right){x}-12a+51$
23.2-a2
23.2-a
$2$
$2$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
23.2
\( 23 \)
\( 23 \)
$1.71718$
$(a-7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$1.329353927$
$38.88510373$
2.945428784
\( \frac{1224298528787}{23} a + \frac{4759445456035}{23} \)
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 56 a - 273\) , \( -394 a + 1920\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(56a-273\right){x}-394a+1920$
23.2-b1
23.2-b
$2$
$2$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
23.2
\( 23 \)
\( 23^{2} \)
$1.71718$
$(a-7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$5.199911754$
$4.540262683$
2.690491294
\( -\frac{41151093}{529} a - \frac{160022908}{529} \)
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 2 a + 9\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(2a+9\right){x}$
23.2-b2
23.2-b
$2$
$2$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
23.2
\( 23 \)
\( 23 \)
$1.71718$
$(a-7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 1 \)
$10.39982350$
$4.540262683$
2.690491294
\( \frac{1224298528787}{23} a + \frac{4759445456035}{23} \)
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -8 a - 36\) , \( -73 a - 294\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-8a-36\right){x}-73a-294$
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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.