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
92.1-a1
92.1-a
$3$
$9$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
92.1
\( 2^{2} \cdot 23 \)
\( 2^{4} \cdot 23 \)
$0.91787$
$(a+4), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 2 \)
$1$
$8.238724756$
1.104030657
\( \frac{36793}{92} a + \frac{210163}{92} \)
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -a - 1\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}$
92.1-a2
92.1-a
$3$
$9$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
92.1
\( 2^{2} \cdot 23 \)
\( 2^{4} \cdot 23^{9} \)
$0.91787$
$(a+4), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 2 \)
$1$
$0.915413861$
1.104030657
\( -\frac{34638770834904571}{3602305322926} a + \frac{53455263008615953}{7204610645852} \)
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 24 a - 96\) , \( 116 a - 322\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(24a-96\right){x}+116a-322$
92.1-a3
92.1-a
$3$
$9$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
92.1
\( 2^{2} \cdot 23 \)
\( 2^{12} \cdot 23^{3} \)
$0.91787$
$(a+4), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Cs.1.1
$1$
\( 2 \cdot 3 \)
$1$
$2.746241585$
1.104030657
\( \frac{4146024701}{389344} a - \frac{1186600043}{778688} \)
\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 4 a + 4\) , \( 4 a - 18\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(4a+4\right){x}+4a-18$
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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.