Atkin-Lehner |
2+ 3+ 5- 17- |
Signs for the Atkin-Lehner involutions |
Class |
69360w |
Isogeny class |
Conductor |
69360 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
822528 |
Modular degree for the optimal curve |
Δ |
-83709089292000000 = -1 · 28 · 3 · 56 · 178 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -5 0 -1 17- 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-126100,22196752] |
[a1,a2,a3,a4,a6] |
Generators |
[-96:5780:1] |
Generators of the group modulo torsion |
j |
-124176976/46875 |
j-invariant |
L |
3.8959197988779 |
L(r)(E,1)/r! |
Ω |
0.32107997216812 |
Real period |
R |
0.33704996831612 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999969571 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34680bb1 69360bg1 |
Quadratic twists by: -4 17 |