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
88.4-a1
88.4-a
$4$
$6$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
88.4
\( 2^{3} \cdot 11 \)
\( 2^{7} \cdot 11^{2} \)
$0.72412$
$(a), (-a+1), (2a+1)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1
$1$
\( 2 \cdot 3 \)
$1$
$5.029489152$
0.633656072
\( -\frac{1374871}{968} a - \frac{22437003}{484} \)
\( \bigl[a\) , \( -a\) , \( 0\) , \( -2 a - 1\) , \( -a\bigr] \)
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-2a-1\right){x}-a$
88.4-a2
88.4-a
$4$
$6$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
88.4
\( 2^{3} \cdot 11 \)
\( 2^{13} \cdot 11^{6} \)
$0.72412$
$(a), (-a+1), (2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.2
$1$
\( 2 \)
$1$
$1.676496384$
0.633656072
\( -\frac{2638880885903}{907039232} a - \frac{10019801056547}{453519616} \)
\( \bigl[a\) , \( -a\) , \( 0\) , \( 3 a - 31\) , \( -2 a + 74\bigr] \)
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(3a-31\right){x}-2a+74$
88.4-a3
88.4-a
$4$
$6$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
88.4
\( 2^{3} \cdot 11 \)
\( 2^{26} \cdot 11^{3} \)
$0.72412$
$(a), (-a+1), (2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.2
$1$
\( 2 \)
$1$
$1.676496384$
0.633656072
\( -\frac{198874755649}{348913664} a + \frac{23956044435}{174456832} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( 4 a + 10\) , \( 21 a - 19\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(4a+10\right){x}+21a-19$
88.4-a4
88.4-a
$4$
$6$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
88.4
\( 2^{3} \cdot 11 \)
\( 2^{14} \cdot 11 \)
$0.72412$
$(a), (-a+1), (2a+1)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1
$1$
\( 2 \cdot 3 \)
$1$
$5.029489152$
0.633656072
\( \frac{328039}{704} a + \frac{31003}{352} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -a\) , \( -a + 1\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}-a+1$
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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.