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
7.2-a6
7.2-a
$6$
$8$
6.6.1279733.1
$6$
$[6, 0]$
7.2
\( 7 \)
\( - 7^{2} \)
$118.88391$
$(-a^4+a^3+4a^2-a-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$256$
\( 2 \)
$1$
$10.75704577$
1.21715
\( \frac{1307780824025356872024765295948965037006665607}{7} a^{5} - \frac{1426930782360125700490308291091787017129909047}{7} a^{4} - \frac{9143610193366820283442749807521617239815916698}{7} a^{3} + \frac{4767258720016713504152715749572825371641060421}{7} a^{2} + \frac{17410729135899459869092701189140814182089683462}{7} a + \frac{1438874534605637964988709222541326697190256371}{7} \)
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 3 a\) , \( a^{4} - 4 a^{2} - a + 1\) , \( 145 a^{5} - 16 a^{4} - 824 a^{3} - 170 a^{2} + 797 a - 38\) , \( -6563 a^{5} - 813 a^{4} + 37612 a^{3} + 13925 a^{2} - 35646 a - 2732\bigr] \)
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+3\right){x}{y}+\left(a^{4}-4a^{2}-a+1\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+3a\right){x}^{2}+\left(145a^{5}-16a^{4}-824a^{3}-170a^{2}+797a-38\right){x}-6563a^{5}-813a^{4}+37612a^{3}+13925a^{2}-35646a-2732$
7.2-d6
7.2-d
$6$
$8$
6.6.1279733.1
$6$
$[6, 0]$
7.2
\( 7 \)
\( - 7^{2} \)
$118.88391$
$(-a^4+a^3+4a^2-a-1)$
$0 \le r \le 5$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
\( 2 \)
$1$
$0.956453280$
2.62611
\( \frac{1307780824025356872024765295948965037006665607}{7} a^{5} - \frac{1426930782360125700490308291091787017129909047}{7} a^{4} - \frac{9143610193366820283442749807521617239815916698}{7} a^{3} + \frac{4767258720016713504152715749572825371641060421}{7} a^{2} + \frac{17410729135899459869092701189140814182089683462}{7} a + \frac{1438874534605637964988709222541326697190256371}{7} \)
\( \bigl[a^{5} - 2 a^{4} - 2 a^{3} + 5 a^{2} - 2 a - 1\) , \( -a^{5} + a^{4} + 3 a^{3} - a^{2} + a - 2\) , \( a\) , \( 48 a^{5} - 57 a^{4} - 384 a^{3} + 429 a^{2} + 713 a - 758\) , \( 724 a^{5} - 1072 a^{4} - 4688 a^{3} + 5920 a^{2} + 7542 a - 8105\bigr] \)
${y}^2+\left(a^{5}-2a^{4}-2a^{3}+5a^{2}-2a-1\right){x}{y}+a{y}={x}^{3}+\left(-a^{5}+a^{4}+3a^{3}-a^{2}+a-2\right){x}^{2}+\left(48a^{5}-57a^{4}-384a^{3}+429a^{2}+713a-758\right){x}+724a^{5}-1072a^{4}-4688a^{3}+5920a^{2}+7542a-8105$
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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.