Atkin-Lehner |
2- 3+ 17+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
67728m |
Isogeny class |
Conductor |
67728 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
57600 |
Modular degree for the optimal curve |
Δ |
138706944 = 215 · 3 · 17 · 83 |
Discriminant |
Eigenvalues |
2- 3+ -3 -2 -2 -3 17+ 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-5072,140736] |
[a1,a2,a3,a4,a6] |
Generators |
[-75:306:1] [40:-16:1] |
Generators of the group modulo torsion |
j |
3523604223313/33864 |
j-invariant |
L |
6.5997238982932 |
L(r)(E,1)/r! |
Ω |
1.6621066062644 |
Real period |
R |
0.99267457836375 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000025 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8466m1 |
Quadratic twists by: -4 |