Atkin-Lehner |
2- 3+ 5+ 17+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
56610p |
Isogeny class |
Conductor |
56610 |
Conductor |
∏ cp |
144 |
Product of Tamagawa factors cp |
deg |
829440 |
Modular degree for the optimal curve |
Δ |
-341759913984000000 = -1 · 218 · 33 · 56 · 174 · 37 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 0 -2 6 17+ 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,129142,-21758519] |
[a1,a2,a3,a4,a6] |
Generators |
[253:5075:1] |
Generators of the group modulo torsion |
j |
8821970975423595933/12657774592000000 |
j-invariant |
L |
9.5388398335848 |
L(r)(E,1)/r! |
Ω |
0.16117999488603 |
Real period |
R |
1.6439246901593 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000085 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
56610a1 |
Quadratic twists by: -3 |