Atkin-Lehner |
2- 3+ 13- 47- |
Signs for the Atkin-Lehner involutions |
Class |
47658z |
Isogeny class |
Conductor |
47658 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
89856 |
Modular degree for the optimal curve |
Δ |
-394155298368 = -1 · 26 · 33 · 133 · 473 |
Discriminant |
Eigenvalues |
2- 3+ 0 -3 -3 13- -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-10423,406349] |
[a1,a2,a3,a4,a6] |
Generators |
[-922:2901:8] [61:16:1] |
Generators of the group modulo torsion |
j |
-56999949734125/179406144 |
j-invariant |
L |
10.899529707887 |
L(r)(E,1)/r! |
Ω |
0.95270566392068 |
Real period |
R |
0.31779459866127 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999994 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47658g1 |
Quadratic twists by: 13 |