Atkin-Lehner |
2- 3- 5+ 11- 89- |
Signs for the Atkin-Lehner involutions |
Class |
29370bh |
Isogeny class |
Conductor |
29370 |
Conductor |
∏ cp |
256 |
Product of Tamagawa factors cp |
deg |
2703360 |
Modular degree for the optimal curve |
Δ |
282621636000000 = 28 · 38 · 56 · 112 · 89 |
Discriminant |
Eigenvalues |
2- 3- 5+ -2 11- -4 -2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-190080996,-1008702232560] |
[a1,a2,a3,a4,a6] |
Generators |
[-54597678:27295464:6859] |
Generators of the group modulo torsion |
j |
759521040149442590077955416129/282621636000000 |
j-invariant |
L |
8.8308104427978 |
L(r)(E,1)/r! |
Ω |
0.040659766469592 |
Real period |
R |
3.3935613789594 |
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 |
88110bf1 |
Quadratic twists by: -3 |