Atkin-Lehner |
2+ 3- 7- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
69384k |
Isogeny class |
Conductor |
69384 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
147456 |
Modular degree for the optimal curve |
Δ |
6996821328 = 24 · 32 · 77 · 59 |
Discriminant |
Eigenvalues |
2+ 3- 2 7- 0 -2 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-60727,5739782] |
[a1,a2,a3,a4,a6] |
Generators |
[61988:1873005:64] |
Generators of the group modulo torsion |
j |
13157340731392/3717 |
j-invariant |
L |
9.6014643392168 |
L(r)(E,1)/r! |
Ω |
1.0642560001564 |
Real period |
R |
9.0217619984696 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000378 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
9912b1 |
Quadratic twists by: -7 |