Atkin-Lehner |
2- 3+ 7+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
48048bd |
Isogeny class |
Conductor |
48048 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
248832 |
Modular degree for the optimal curve |
Δ |
1141040841228288 = 218 · 33 · 7 · 116 · 13 |
Discriminant |
Eigenvalues |
2- 3+ 0 7+ 11+ 13- 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-57608,-5048592] |
[a1,a2,a3,a4,a6] |
Generators |
[298548:4603456:729] |
Generators of the group modulo torsion |
j |
5162020164015625/278574424128 |
j-invariant |
L |
5.115196113346 |
L(r)(E,1)/r! |
Ω |
0.30919689567395 |
Real period |
R |
8.2717455849576 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999978 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6006q1 |
Quadratic twists by: -4 |