Atkin-Lehner |
2- 3+ 7- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
68544dd |
Isogeny class |
Conductor |
68544 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
86016 |
Modular degree for the optimal curve |
Δ |
-940047510528 = -1 · 210 · 33 · 76 · 172 |
Discriminant |
Eigenvalues |
2- 3+ -2 7- -6 -2 17+ 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-216,-46664] |
[a1,a2,a3,a4,a6] |
Generators |
[66:476:1] |
Generators of the group modulo torsion |
j |
-40310784/34000561 |
j-invariant |
L |
3.7242390865618 |
L(r)(E,1)/r! |
Ω |
0.39786828243854 |
Real period |
R |
0.78004020649671 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000697 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68544e1 17136a1 68544dg1 |
Quadratic twists by: -4 8 -3 |