Atkin-Lehner |
2+ 3- 7- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
69384j |
Isogeny class |
Conductor |
69384 |
Conductor |
∏ cp |
88 |
Product of Tamagawa factors cp |
deg |
8110080 |
Modular degree for the optimal curve |
Δ |
7.2586913571563E+21 |
Discriminant |
Eigenvalues |
2+ 3- 0 7- 4 0 -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-170396928,-856179037008] |
[a1,a2,a3,a4,a6] |
Generators |
[127731:45402126:1] |
Generators of the group modulo torsion |
j |
4541724645902232578500/60251814962073 |
j-invariant |
L |
8.1545228395658 |
L(r)(E,1)/r! |
Ω |
0.041786352153507 |
Real period |
R |
8.8703634074996 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998871 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
9912d1 |
Quadratic twists by: -7 |