Atkin-Lehner |
2+ 3+ 13+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
69966a |
Isogeny class |
Conductor |
69966 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
129024 |
Modular degree for the optimal curve |
Δ |
9975508238592 = 28 · 33 · 137 · 23 |
Discriminant |
Eigenvalues |
2+ 3+ 0 0 4 13+ 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-5862,-80716] |
[a1,a2,a3,a4,a6] |
Generators |
[-29:268:1] |
Generators of the group modulo torsion |
j |
170953875/76544 |
j-invariant |
L |
5.3984694705838 |
L(r)(E,1)/r! |
Ω |
0.56888685131044 |
Real period |
R |
0.59309569400647 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
4.0000000002651 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69966v1 5382h1 |
Quadratic twists by: -3 13 |