Atkin-Lehner |
2+ 3+ 5+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
31200h |
Isogeny class |
Conductor |
31200 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
16384 |
Modular degree for the optimal curve |
Δ |
1053000000 = 26 · 34 · 56 · 13 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ -2 -6 13- 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-358,2212] |
[a1,a2,a3,a4,a6] |
Generators |
[-18:50:1] [-9:68:1] |
Generators of the group modulo torsion |
j |
5088448/1053 |
j-invariant |
L |
6.8314807217237 |
L(r)(E,1)/r! |
Ω |
1.4712767301033 |
Real period |
R |
2.321616519159 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999996 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
31200cd1 62400cl2 93600ej1 1248i1 |
Quadratic twists by: -4 8 -3 5 |