Atkin-Lehner |
2- 3+ 11+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
48576bx |
Isogeny class |
Conductor |
48576 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
122880 |
Modular degree for the optimal curve |
Δ |
26326059319296 = 217 · 38 · 113 · 23 |
Discriminant |
Eigenvalues |
2- 3+ -1 1 11+ -5 -7 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-7521,-43263] |
[a1,a2,a3,a4,a6] |
Generators |
[-83:48:1] [-21:324:1] |
Generators of the group modulo torsion |
j |
359003179442/200851893 |
j-invariant |
L |
7.8550326198058 |
L(r)(E,1)/r! |
Ω |
0.55073388125218 |
Real period |
R |
1.7828557691842 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
48576bs1 12144i1 |
Quadratic twists by: -4 8 |