Atkin-Lehner |
31- 41- |
Signs for the Atkin-Lehner involutions |
Class |
1271a |
Isogeny class |
Conductor |
1271 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
72 |
Modular degree for the optimal curve |
Δ |
39401 = 312 · 41 |
Discriminant |
Eigenvalues |
1 0 2 2 -4 -4 -4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-11,-8] |
[a1,a2,a3,a4,a6] |
Generators |
[-18:19:8] |
Generators of the group modulo torsion |
j |
154854153/39401 |
j-invariant |
L |
3.373951025244 |
L(r)(E,1)/r! |
Ω |
2.6593937085165 |
Real period |
R |
2.5373836257784 |
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 |
20336b1 81344g1 11439f1 31775h1 |
Quadratic twists by: -4 8 -3 5 |