Atkin-Lehner |
2+ 3+ 11- 59- |
Signs for the Atkin-Lehner involutions |
Class |
11682b |
Isogeny class |
Conductor |
11682 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
22528 |
Modular degree for the optimal curve |
Δ |
67754852352 = 216 · 33 · 11 · 592 |
Discriminant |
Eigenvalues |
2+ 3+ -4 2 11- 6 2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-2649,51629] |
[a1,a2,a3,a4,a6] |
Generators |
[35:12:1] |
Generators of the group modulo torsion |
j |
76154932854603/2509438976 |
j-invariant |
L |
2.9098339737887 |
L(r)(E,1)/r! |
Ω |
1.092603697352 |
Real period |
R |
1.3316054031489 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
93456s1 11682m1 128502bj1 |
Quadratic twists by: -4 -3 -11 |