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
88.8-a1
88.8-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
88.8
\( 2^{3} \cdot 11 \)
\( 2^{10} \cdot 11^{2} \)
$0.72412$
$(-a+1), (2a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$5.265414026$
0.995069718
\( -\frac{5145}{121} a + \frac{5831}{121} \)
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -a\) , \( -a + 1\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}-a+1$
88.8-a2
88.8-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
88.8
\( 2^{3} \cdot 11 \)
\( 2^{11} \cdot 11^{4} \)
$0.72412$
$(-a+1), (2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$2.632707013$
0.995069718
\( -\frac{650842199}{14641} a + \frac{483496007}{14641} \)
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 4 a - 15\) , \( -15 a + 19\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(4a-15\right){x}-15a+19$
88.8-a3
88.8-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
88.8
\( 2^{3} \cdot 11 \)
\( 2^{11} \cdot 11 \)
$0.72412$
$(-a+1), (2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 1 \)
$1$
$5.265414026$
0.995069718
\( \frac{57099}{11} a + \frac{132553}{11} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+{x}$
88.8-a4
88.8-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
88.8
\( 2^{3} \cdot 11 \)
\( 2^{8} \cdot 11 \)
$0.72412$
$(-a+1), (2a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$5.265414026$
0.995069718
\( \frac{1102675}{11} a + \frac{483183}{11} \)
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -3 a + 5\) , \( a + 1\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-3a+5\right){x}+a+1$
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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.