Atkin-Lehner |
2+ 13- 103- |
Signs for the Atkin-Lehner involutions |
Class |
85696z |
Isogeny class |
Conductor |
85696 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
129024 |
Modular degree for the optimal curve |
Δ |
1437740302336 = 230 · 13 · 103 |
Discriminant |
Eigenvalues |
2+ -1 -1 -4 0 13- 3 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-5441,-141503] |
[a1,a2,a3,a4,a6] |
Generators |
[-33:32:1] |
Generators of the group modulo torsion |
j |
67967263441/5484544 |
j-invariant |
L |
3.5282749526793 |
L(r)(E,1)/r! |
Ω |
0.55871766559125 |
Real period |
R |
3.1574757413639 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000005463 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85696ca1 2678k1 |
Quadratic twists by: -4 8 |