Atkin-Lehner |
2- 3- 5+ 13+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
47970bc |
Isogeny class |
Conductor |
47970 |
Conductor |
∏ cp |
224 |
Product of Tamagawa factors cp |
deg |
344064 |
Modular degree for the optimal curve |
Δ |
-12234882816000000 = -1 · 214 · 37 · 56 · 13 · 412 |
Discriminant |
Eigenvalues |
2- 3- 5+ -2 0 13+ 4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-35708,-5912769] |
[a1,a2,a3,a4,a6] |
Generators |
[293:2805:1] |
Generators of the group modulo torsion |
j |
-6906871239936121/16783104000000 |
j-invariant |
L |
7.6698963357991 |
L(r)(E,1)/r! |
Ω |
0.16193416345779 |
Real period |
R |
0.84579085501851 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000012 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
15990f1 |
Quadratic twists by: -3 |