Atkin-Lehner |
2+ 37+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
12136a |
Isogeny class |
Conductor |
12136 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
2688 |
Modular degree for the optimal curve |
Δ |
57476096 = 210 · 372 · 41 |
Discriminant |
Eigenvalues |
2+ -2 2 0 2 2 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-112,240] |
[a1,a2,a3,a4,a6] |
Generators |
[20:80:1] |
Generators of the group modulo torsion |
j |
153091012/56129 |
j-invariant |
L |
3.8224990965134 |
L(r)(E,1)/r! |
Ω |
1.8126739079337 |
Real period |
R |
2.1087626846633 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
24272a1 97088h1 109224h1 |
Quadratic twists by: -4 8 -3 |