Atkin-Lehner |
2- 3- 5+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
48510dl |
Isogeny class |
Conductor |
48510 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
286720 |
Modular degree for the optimal curve |
Δ |
-3203596187876700 = -1 · 22 · 38 · 52 · 79 · 112 |
Discriminant |
Eigenvalues |
2- 3- 5+ 7- 11- 4 -6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-8168,2740007] |
[a1,a2,a3,a4,a6] |
Generators |
[-586:14009:8] |
Generators of the group modulo torsion |
j |
-2048383/108900 |
j-invariant |
L |
9.2907296980183 |
L(r)(E,1)/r! |
Ω |
0.37119041734458 |
Real period |
R |
3.1286939478588 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000027 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
16170ba1 48510ei1 |
Quadratic twists by: -3 -7 |