Atkin-Lehner |
2- 11- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
4048i |
Isogeny class |
Conductor |
4048 |
Conductor |
∏ cp |
14 |
Product of Tamagawa factors cp |
deg |
68544 |
Modular degree for the optimal curve |
Δ |
14686779244544 = 215 · 117 · 23 |
Discriminant |
Eigenvalues |
2- 0 -3 -3 11- 5 5 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-4648979,-3858197806] |
[a1,a2,a3,a4,a6] |
Generators |
[-155605:242:125] |
Generators of the group modulo torsion |
j |
2712917065234165678953/3585639464 |
j-invariant |
L |
2.6972103233542 |
L(r)(E,1)/r! |
Ω |
0.10281587091252 |
Real period |
R |
1.8738146020619 |
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 |
506b1 16192p1 36432bw1 101200bu1 |
Quadratic twists by: -4 8 -3 5 |