Atkin-Lehner |
2- 3+ 7- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
48048bw |
Isogeny class |
Conductor |
48048 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
61440 |
Modular degree for the optimal curve |
Δ |
-5403467317248 = -1 · 222 · 32 · 7 · 112 · 132 |
Discriminant |
Eigenvalues |
2- 3+ 0 7- 11- 13- 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,1672,108144] |
[a1,a2,a3,a4,a6] |
Generators |
[-14:286:1] |
Generators of the group modulo torsion |
j |
126128378375/1319205888 |
j-invariant |
L |
5.1133520876745 |
L(r)(E,1)/r! |
Ω |
0.5613195088901 |
Real period |
R |
1.1386901770463 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000027 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6006k1 |
Quadratic twists by: -4 |