Atkin-Lehner |
2- 3+ 11- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
48642r |
Isogeny class |
Conductor |
48642 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
322560 |
Modular degree for the optimal curve |
Δ |
2523296414883684 = 22 · 3 · 1112 · 67 |
Discriminant |
Eigenvalues |
2- 3+ -2 0 11- -2 4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-107874,13376331] |
[a1,a2,a3,a4,a6] |
Generators |
[27699:768123:343] |
Generators of the group modulo torsion |
j |
78364289651257/1424335044 |
j-invariant |
L |
6.0583035586716 |
L(r)(E,1)/r! |
Ω |
0.45757818865175 |
Real period |
R |
6.619965405804 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000035 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4422a1 |
Quadratic twists by: -11 |