Atkin-Lehner |
2- 3- 13- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
71136bl |
Isogeny class |
Conductor |
71136 |
Conductor |
∏ cp |
112 |
Product of Tamagawa factors cp |
deg |
817152 |
Modular degree for the optimal curve |
Δ |
-10679865863786496 = -1 · 212 · 37 · 137 · 19 |
Discriminant |
Eigenvalues |
2- 3- -3 -3 -4 13- 6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-321564,70361696] |
[a1,a2,a3,a4,a6] |
Generators |
[373:-1521:1] [334:468:1] |
Generators of the group modulo torsion |
j |
-1231511588068672/3576665469 |
j-invariant |
L |
7.8320348501084 |
L(r)(E,1)/r! |
Ω |
0.40680646205483 |
Real period |
R |
0.17189717743656 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000011 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
71136t1 23712f1 |
Quadratic twists by: -4 -3 |