Atkin-Lehner |
3+ 7+ 11- 89- |
Signs for the Atkin-Lehner involutions |
Class |
20559a |
Isogeny class |
Conductor |
20559 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
8640 |
Modular degree for the optimal curve |
Δ |
-4231473939 = -1 · 36 · 72 · 113 · 89 |
Discriminant |
Eigenvalues |
0 3+ -1 7+ 11- 7 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,399,-772] |
[a1,a2,a3,a4,a6] |
Generators |
[24:148:1] |
Generators of the group modulo torsion |
j |
7007344787456/4231473939 |
j-invariant |
L |
3.397275377937 |
L(r)(E,1)/r! |
Ω |
0.8049289145956 |
Real period |
R |
0.3517158799507 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61677a1 |
Quadratic twists by: -3 |