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-a3
91.1-a
$8$
$16$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
91.1
\( 7 \cdot 13 \)
\( 7^{2} \cdot 13^{4} \)
$1.32661$
$(-a^2-a+2), (-2a^2+a+2)$
0
$\Z/2\Z\oplus\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$145.8010047$
0.650897342
\( -\frac{3698907677516}{199927} a^{2} + \frac{293174005427}{28561} a + \frac{8312780816110}{199927} \)
\( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( -4\) , \( -3 a^{2} - a + 9\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}-4{x}-3a^{2}-a+9$
637.3-a3
637.3-a
$8$
$16$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
637.3
\( 7^{2} \cdot 13 \)
\( 7^{8} \cdot 13^{4} \)
$1.83482$
$(-a^2-a+2), (-2a^2+a+2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$15.69527055$
1.121090754
\( -\frac{3698907677516}{199927} a^{2} + \frac{293174005427}{28561} a + \frac{8312780816110}{199927} \)
\( \bigl[a^{2} + a - 1\) , \( -a^{2} + 3\) , \( a + 1\) , \( -19 a^{2} + 24 a - 7\) , \( -44 a^{2} + 97 a - 39\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-19a^{2}+24a-7\right){x}-44a^{2}+97a-39$
1183.5-c5
1183.5-c
$8$
$16$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
1183.5
\( 7 \cdot 13^{2} \)
\( 7^{2} \cdot 13^{10} \)
$2.03423$
$(-a^2-a+2), (-2a^2+a+2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$16.79636781$
1.199740558
\( -\frac{3698907677516}{199927} a^{2} + \frac{293174005427}{28561} a + \frac{8312780816110}{199927} \)
\( \bigl[a + 1\) , \( 1\) , \( a^{2} + a - 1\) , \( -28 a^{2} + 51 a - 23\) , \( 96 a^{2} - 212 a + 65\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+{x}^{2}+\left(-28a^{2}+51a-23\right){x}+96a^{2}-212a+65$
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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.