Atkin-Lehner |
2- 3- 5- 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68970cr |
Isogeny class |
Conductor |
68970 |
Conductor |
∏ cp |
936 |
Product of Tamagawa factors cp |
deg |
1257984 |
Modular degree for the optimal curve |
Δ |
-3351942000000000000 = -1 · 213 · 36 · 512 · 112 · 19 |
Discriminant |
Eigenvalues |
2- 3- 5- 1 11- 1 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-222615,-96938775] |
[a1,a2,a3,a4,a6] |
Generators |
[1830:74085:1] |
Generators of the group modulo torsion |
j |
-10083277886982294841/27702000000000000 |
j-invariant |
L |
14.279221183809 |
L(r)(E,1)/r! |
Ω |
0.10196459168859 |
Real period |
R |
0.14961642992433 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000453 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68970be1 |
Quadratic twists by: -11 |