Atkin-Lehner |
2- 3- 5- 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
129360ho |
Isogeny class |
Conductor |
129360 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
497664 |
Modular degree for the optimal curve |
Δ |
-947061273312000 = -1 · 28 · 33 · 53 · 77 · 113 |
Discriminant |
Eigenvalues |
2- 3- 5- 7- 11+ -2 3 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,12675,1379223] |
[a1,a2,a3,a4,a6] |
Generators |
[51:-1470:1] |
Generators of the group modulo torsion |
j |
7476617216/31444875 |
j-invariant |
L |
8.9247333625213 |
L(r)(E,1)/r! |
Ω |
0.3544565939338 |
Real period |
R |
0.34970327341718 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999073907 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
32340t1 18480bk1 |
Quadratic twists by: -4 -7 |