Atkin-Lehner |
2+ 3- 5+ 7- |
Signs for the Atkin-Lehner involutions |
Class |
117600dc |
Isogeny class |
Conductor |
117600 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
589824 |
Modular degree for the optimal curve |
Δ |
1297080225000000 = 26 · 32 · 58 · 78 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 7- 4 6 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-32258,-1414512] |
[a1,a2,a3,a4,a6] |
Generators |
[-45783:442000:729] |
Generators of the group modulo torsion |
j |
31554496/11025 |
j-invariant |
L |
10.389457709856 |
L(r)(E,1)/r! |
Ω |
0.36644497793669 |
Real period |
R |
7.088006594867 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000027692 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
117600fh1 23520bk1 16800d1 |
Quadratic twists by: -4 5 -7 |