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
91.1-a5
91.1-a
$8$
$16$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
91.1
\( 7 \cdot 13 \)
\( - 7 \cdot 13^{2} \)
$1.32661$
$(-a^2-a+2), (-2a^2+a+2)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$145.8010047$
0.650897342
\( \frac{3379823}{1183} a^{2} - \frac{1448892}{1183} a - \frac{6890188}{1183} \)
\( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( 1\) , \( 0\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+{x}$
637.3-a4
637.3-a
$8$
$16$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
637.3
\( 7^{2} \cdot 13 \)
\( - 7^{7} \cdot 13^{2} \)
$1.83482$
$(-a^2-a+2), (-2a^2+a+2)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$15.69527055$
1.121090754
\( \frac{3379823}{1183} a^{2} - \frac{1448892}{1183} a - \frac{6890188}{1183} \)
\( \bigl[a^{2} + a - 1\) , \( -a^{2} + 3\) , \( a + 1\) , \( a^{2} - a + 3\) , \( 7 a - 3\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(a^{2}-a+3\right){x}+7a-3$
1183.5-c6
1183.5-c
$8$
$16$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
1183.5
\( 7 \cdot 13^{2} \)
\( - 7 \cdot 13^{8} \)
$2.03423$
$(-a^2-a+2), (-2a^2+a+2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$16.79636781$
1.199740558
\( \frac{3379823}{1183} a^{2} - \frac{1448892}{1183} a - \frac{6890188}{1183} \)
\( \bigl[a + 1\) , \( 1\) , \( a^{2} + a - 1\) , \( 2 a^{2} - 4 a + 2\) , \( 9 a^{2} - 18 a + 6\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+{x}^{2}+\left(2a^{2}-4a+2\right){x}+9a^{2}-18a+6$
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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.