Atkin-Lehner |
2+ 3- 7+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
48048r |
Isogeny class |
Conductor |
48048 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
133120 |
Modular degree for the optimal curve |
Δ |
-32260953252528 = -1 · 24 · 35 · 74 · 112 · 134 |
Discriminant |
Eigenvalues |
2+ 3- -2 7+ 11+ 13- 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,7041,-149220] |
[a1,a2,a3,a4,a6] |
Generators |
[72:858:1] |
Generators of the group modulo torsion |
j |
2412376450009088/2016309578283 |
j-invariant |
L |
6.3156677955773 |
L(r)(E,1)/r! |
Ω |
0.36340932162942 |
Real period |
R |
0.86894686234971 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000011 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
24024h1 |
Quadratic twists by: -4 |