Atkin-Lehner |
2- 5+ 7- |
Signs for the Atkin-Lehner involutions |
Class |
78400hf |
Isogeny class |
Conductor |
78400 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
-18890099916800 = -1 · 217 · 52 · 78 |
Discriminant |
Eigenvalues |
2- 1 5+ 7- -1 6 7 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-32993,-2327137] |
[a1,a2,a3,a4,a6] |
Generators |
[2279:108464:1] |
Generators of the group modulo torsion |
j |
-10303010/49 |
j-invariant |
L |
8.3158053594232 |
L(r)(E,1)/r! |
Ω |
0.17706774410141 |
Real period |
R |
5.8704970522044 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001348 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
78400bm1 19600o1 78400km1 11200bz1 |
Quadratic twists by: -4 8 5 -7 |