Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696df |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
49152 |
Modular degree for the optimal curve |
Δ |
-5780865024 = -1 · 216 · 36 · 112 |
Discriminant |
Eigenvalues |
2+ 3- 3 -4 11- 3 3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-396,-4752] |
[a1,a2,a3,a4,a6] |
Generators |
[102:1008:1] |
Generators of the group modulo torsion |
j |
-1188 |
j-invariant |
L |
7.8951040722548 |
L(r)(E,1)/r! |
Ω |
0.51673653555133 |
Real period |
R |
1.9098475550541 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000021 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69696gt1 8712m1 7744e1 69696de1 |
Quadratic twists by: -4 8 -3 -11 |