Atkin-Lehner |
2+ 3+ 11- 67- |
Signs for the Atkin-Lehner involutions |
Class |
48642j |
Isogeny class |
Conductor |
48642 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
8640 |
Modular degree for the optimal curve |
Δ |
11820006 = 2 · 36 · 112 · 67 |
Discriminant |
Eigenvalues |
2+ 3+ -1 -1 11- -2 -3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-68,114] |
[a1,a2,a3,a4,a6] |
Generators |
[-1:14:1] |
Generators of the group modulo torsion |
j |
294039889/97686 |
j-invariant |
L |
2.313222270658 |
L(r)(E,1)/r! |
Ω |
2.0831216466376 |
Real period |
R |
0.55522976164471 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999088 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
48642u1 |
Quadratic twists by: -11 |