Atkin-Lehner |
2- 3- 5+ 71- |
Signs for the Atkin-Lehner involutions |
Class |
51120bi |
Isogeny class |
Conductor |
51120 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
518400 |
Modular degree for the optimal curve |
Δ |
66251520000000000 = 217 · 36 · 510 · 71 |
Discriminant |
Eigenvalues |
2- 3- 5+ -3 2 -1 -8 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-159123,21060178] |
[a1,a2,a3,a4,a6] |
Generators |
[-321:6250:1] [-39:5216:1] |
Generators of the group modulo torsion |
j |
149222774347921/22187500000 |
j-invariant |
L |
8.7225534917717 |
L(r)(E,1)/r! |
Ω |
0.33392316159975 |
Real period |
R |
3.2651798732611 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6390d1 5680h1 |
Quadratic twists by: -4 -3 |