Atkin-Lehner |
2+ 3+ 23- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
48024a |
Isogeny class |
Conductor |
48024 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
7424 |
Modular degree for the optimal curve |
Δ |
-6627312 = -1 · 24 · 33 · 232 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ 0 -3 -5 1 -3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-75,279] |
[a1,a2,a3,a4,a6] |
Generators |
[-9:15:1] [-5:23:1] |
Generators of the group modulo torsion |
j |
-108000000/15341 |
j-invariant |
L |
8.6244937689114 |
L(r)(E,1)/r! |
Ω |
2.294511094865 |
Real period |
R |
0.46984376041006 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999995 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
96048a1 48024g1 |
Quadratic twists by: -4 -3 |