Atkin-Lehner |
3- 5+ 17- 89- |
Signs for the Atkin-Lehner involutions |
Class |
68085g |
Isogeny class |
Conductor |
68085 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
55296 |
Modular degree for the optimal curve |
Δ |
-465318421875 = -1 · 39 · 56 · 17 · 89 |
Discriminant |
Eigenvalues |
0 3- 5+ -1 -3 -4 17- 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,1932,-2961] |
[a1,a2,a3,a4,a6] |
Generators |
[59:562:1] [21:216:1] |
Generators of the group modulo torsion |
j |
1094000574464/638296875 |
j-invariant |
L |
7.6374762490494 |
L(r)(E,1)/r! |
Ω |
0.55233273186172 |
Real period |
R |
3.4569181801317 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000041 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
22695g1 |
Quadratic twists by: -3 |