Atkin-Lehner |
2+ 3+ 5+ 71- |
Signs for the Atkin-Lehner involutions |
Class |
68160f |
Isogeny class |
Conductor |
68160 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
92160 |
Modular degree for the optimal curve |
Δ |
301858488000 = 26 · 312 · 53 · 71 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 0 -4 -2 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-12076,-506090] |
[a1,a2,a3,a4,a6] |
Generators |
[131:378:1] [-85415:28830:1331] |
Generators of the group modulo torsion |
j |
3043329768767296/4716538875 |
j-invariant |
L |
8.2254552339514 |
L(r)(E,1)/r! |
Ω |
0.45546625428576 |
Real period |
R |
36.118834958838 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000021 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68160u1 34080bi4 |
Quadratic twists by: -4 8 |