Atkin-Lehner |
2+ 7- 11- 67- |
Signs for the Atkin-Lehner involutions |
Class |
82544p |
Isogeny class |
Conductor |
82544 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
718848 |
Modular degree for the optimal curve |
Δ |
386659988856064 = 28 · 73 · 114 · 673 |
Discriminant |
Eigenvalues |
2+ -3 -3 7- 11- 3 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-63199,6041614] |
[a1,a2,a3,a4,a6] |
Generators |
[-227:2948:1] [-183:3388:1] |
Generators of the group modulo torsion |
j |
109047161722866768/1510390581469 |
j-invariant |
L |
5.9272837758827 |
L(r)(E,1)/r! |
Ω |
0.53607134075318 |
Real period |
R |
0.15356796664031 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000308 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
41272a1 |
Quadratic twists by: -4 |