Atkin-Lehner |
2- 3- 29+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
129456bd |
Isogeny class |
Conductor |
129456 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
7766016 |
Modular degree for the optimal curve |
Δ |
7222162582653696 = 28 · 322 · 29 · 31 |
Discriminant |
Eigenvalues |
2- 3- -1 0 4 -2 3 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-237431703,-1408173524926] |
[a1,a2,a3,a4,a6] |
Generators |
[-10263132440213597794004780581443921782994323081594933726753930:2692326792937772634912460938114345900927813769237152734739:1153642948799829271370503052818883183396213497141242583000] |
Generators of the group modulo torsion |
j |
7931810705276935648987216/38699002179 |
j-invariant |
L |
6.9101771572697 |
L(r)(E,1)/r! |
Ω |
0.038460495738061 |
Real period |
R |
89.834738537071 |
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 |
32364h1 43152v1 |
Quadratic twists by: -4 -3 |