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-a4
91.1-a
$8$
$16$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
91.1
\( 7 \cdot 13 \)
\( 7^{4} \cdot 13^{8} \)
$1.32661$
$(-a^2-a+2), (-2a^2+a+2)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$18.22512558$
0.650897342
\( \frac{20917603896641523}{39970805329} a^{2} + \frac{16797981605493841}{39970805329} a - \frac{11327303846528113}{39970805329} \)
\( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( 0\) , \( -15 a^{2} - 5 a + 1\) , \( -49 a^{2} - 26 a + 29\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-15a^{2}-5a+1\right){x}-49a^{2}-26a+29$
637.3-a5
637.3-a
$8$
$16$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
637.3
\( 7^{2} \cdot 13 \)
\( 7^{10} \cdot 13^{8} \)
$1.83482$
$(-a^2-a+2), (-2a^2+a+2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$15.69527055$
1.121090754
\( \frac{20917603896641523}{39970805329} a^{2} + \frac{16797981605493841}{39970805329} a - \frac{11327303846528113}{39970805329} \)
\( \bigl[a^{2} + a - 1\) , \( -a^{2} + 3\) , \( a + 1\) , \( -129 a^{2} + 39 a + 8\) , \( 694 a^{2} - 101 a - 97\bigr] \)
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-129a^{2}+39a+8\right){x}+694a^{2}-101a-97$
1183.5-c4
1183.5-c
$8$
$16$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
1183.5
\( 7 \cdot 13^{2} \)
\( 7^{4} \cdot 13^{14} \)
$2.03423$
$(-a^2-a+2), (-2a^2+a+2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$8.398183907$
1.199740558
\( \frac{20917603896641523}{39970805329} a^{2} + \frac{16797981605493841}{39970805329} a - \frac{11327303846528113}{39970805329} \)
\( \bigl[a + 1\) , \( 1\) , \( a^{2} + a - 1\) , \( -153 a^{2} + 151 a - 43\) , \( -336 a^{2} + 1790 a - 740\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+{x}^{2}+\left(-153a^{2}+151a-43\right){x}-336a^{2}+1790a-740$
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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.