Atkin-Lehner |
2- 3- 5- 11+ 67+ |
Signs for the Atkin-Lehner involutions |
Class |
66330br |
Isogeny class |
Conductor |
66330 |
Conductor |
∏ cp |
768 |
Product of Tamagawa factors cp |
deg |
1179648 |
Modular degree for the optimal curve |
Δ |
255312129600000000 = 212 · 39 · 58 · 112 · 67 |
Discriminant |
Eigenvalues |
2- 3- 5- -4 11+ -6 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-161042,-5226991] |
[a1,a2,a3,a4,a6] |
Generators |
[-383:591:1] [-333:3541:1] |
Generators of the group modulo torsion |
j |
633594096376849369/350222400000000 |
j-invariant |
L |
14.166094986695 |
L(r)(E,1)/r! |
Ω |
0.25518288346065 |
Real period |
R |
1.1565312488314 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000012 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
22110e1 |
Quadratic twists by: -3 |