Atkin-Lehner |
2+ 5+ 11+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
48950d |
Isogeny class |
Conductor |
48950 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
36864 |
Modular degree for the optimal curve |
Δ |
2692250000 = 24 · 56 · 112 · 89 |
Discriminant |
Eigenvalues |
2+ 0 5+ 0 11+ -2 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-5642,164516] |
[a1,a2,a3,a4,a6] |
Generators |
[-56:578:1] [-1:413:1] |
Generators of the group modulo torsion |
j |
1271294679537/172304 |
j-invariant |
L |
6.911004556635 |
L(r)(E,1)/r! |
Ω |
1.3864411460978 |
Real period |
R |
1.246177051238 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999979 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
1958a1 |
Quadratic twists by: 5 |