Atkin-Lehner |
2+ 3+ 7+ 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
48048a |
Isogeny class |
Conductor |
48048 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
131072 |
Modular degree for the optimal curve |
Δ |
-77216863756032 = -1 · 28 · 316 · 72 · 11 · 13 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7+ 11+ 13+ 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-6412,468832] |
[a1,a2,a3,a4,a6] |
Generators |
[-79:690:1] |
Generators of the group modulo torsion |
j |
-113902175120848/301628374047 |
j-invariant |
L |
5.4220221175905 |
L(r)(E,1)/r! |
Ω |
0.53970677665063 |
Real period |
R |
5.0231184340758 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000021 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
24024q1 |
Quadratic twists by: -4 |