Atkin-Lehner |
2- 3+ 7+ 11- 17- |
Signs for the Atkin-Lehner involutions |
Class |
47124b |
Isogeny class |
Conductor |
47124 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
85248 |
Modular degree for the optimal curve |
Δ |
-2025338814576 = -1 · 24 · 39 · 7 · 11 · 174 |
Discriminant |
Eigenvalues |
2- 3+ -3 7+ 11- 3 17- -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1809,74601] |
[a1,a2,a3,a4,a6] |
Generators |
[-56:17:1] [63:459:1] |
Generators of the group modulo torsion |
j |
-2078873856/6431117 |
j-invariant |
L |
8.137878716071 |
L(r)(E,1)/r! |
Ω |
0.72768304041312 |
Real period |
R |
0.46596974370027 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999989 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47124a1 |
Quadratic twists by: -3 |