Atkin-Lehner |
2- 3- 5- 13+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
67860r |
Isogeny class |
Conductor |
67860 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
4521984 |
Modular degree for the optimal curve |
Δ |
3430891247051970000 = 24 · 322 · 54 · 13 · 292 |
Discriminant |
Eigenvalues |
2- 3- 5- 2 -6 13+ 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-20479692,-35672363899] |
[a1,a2,a3,a4,a6] |
Generators |
[12570636:-773415935:1728] |
Generators of the group modulo torsion |
j |
81441631233316171300864/294143625433125 |
j-invariant |
L |
6.4031697517259 |
L(r)(E,1)/r! |
Ω |
0.07096901761527 |
Real period |
R |
11.278107626043 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002326 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
22620a1 |
Quadratic twists by: -3 |