Atkin-Lehner |
2- 3- 7- 13+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
111384cb |
Isogeny class |
Conductor |
111384 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
835584 |
Modular degree for the optimal curve |
Δ |
22166965082113488 = 24 · 312 · 74 · 13 · 174 |
Discriminant |
Eigenvalues |
2- 3- 0 7- -6 13+ 17+ 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-70230,70229] |
[a1,a2,a3,a4,a6] |
Generators |
[-242:1701:1] [-74:2205:1] |
Generators of the group modulo torsion |
j |
3284310482176000/1900459969317 |
j-invariant |
L |
11.973875125256 |
L(r)(E,1)/r! |
Ω |
0.32255644309872 |
Real period |
R |
2.3201123747089 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000002046 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
37128c1 |
Quadratic twists by: -3 |