Atkin-Lehner |
2+ 3- 5- 11- 31- |
Signs for the Atkin-Lehner involutions |
Class |
81840bi |
Isogeny class |
Conductor |
81840 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
239616 |
Modular degree for the optimal curve |
Δ |
5799084192000 = 28 · 312 · 53 · 11 · 31 |
Discriminant |
Eigenvalues |
2+ 3- 5- 0 11- -6 6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-15180,-715572] |
[a1,a2,a3,a4,a6] |
Generators |
[-69:90:1] |
Generators of the group modulo torsion |
j |
1511219924406736/22652672625 |
j-invariant |
L |
8.2452574833233 |
L(r)(E,1)/r! |
Ω |
0.43050042366811 |
Real period |
R |
1.0640404398556 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000585 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
40920i1 |
Quadratic twists by: -4 |