Atkin-Lehner |
3- 5+ 17+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
68085d |
Isogeny class |
Conductor |
68085 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
37632 |
Modular degree for the optimal curve |
Δ |
-1406295675 = -1 · 37 · 52 · 172 · 89 |
Discriminant |
Eigenvalues |
-2 3- 5+ 0 -4 0 17+ 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-3,1804] |
[a1,a2,a3,a4,a6] |
Generators |
[-11:22:1] [16:76:1] |
Generators of the group modulo torsion |
j |
-4096/1929075 |
j-invariant |
L |
5.0669946595576 |
L(r)(E,1)/r! |
Ω |
1.2081191657611 |
Real period |
R |
0.52426478313862 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000021 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
22695c1 |
Quadratic twists by: -3 |