Atkin-Lehner |
2+ 3- 7+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
111552bd |
Isogeny class |
Conductor |
111552 |
Conductor |
∏ cp |
56 |
Product of Tamagawa factors cp |
deg |
559104 |
Modular degree for the optimal curve |
Δ |
9326589640704 = 220 · 37 · 72 · 83 |
Discriminant |
Eigenvalues |
2+ 3- -2 7+ 2 -2 -8 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-241729,45664031] |
[a1,a2,a3,a4,a6] |
Generators |
[290:189:1] [-403:8820:1] |
Generators of the group modulo torsion |
j |
5958978974685073/35578116 |
j-invariant |
L |
12.194414260233 |
L(r)(E,1)/r! |
Ω |
0.64891170197023 |
Real period |
R |
1.3422929303158 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000721 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
111552cs1 3486h1 |
Quadratic twists by: -4 8 |