Atkin-Lehner |
3+ 5- 29- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
69165d |
Isogeny class |
Conductor |
69165 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
883200 |
Modular degree for the optimal curve |
Δ |
-1138385654296875 = -1 · 33 · 510 · 29 · 533 |
Discriminant |
Eigenvalues |
-2 3+ 5- 1 0 -1 2 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-1399407,637185062] |
[a1,a2,a3,a4,a6] |
Generators |
[687:-188:1] |
Generators of the group modulo torsion |
j |
-11225147951993946697728/42162431640625 |
j-invariant |
L |
3.9344825462555 |
L(r)(E,1)/r! |
Ω |
0.42858105762559 |
Real period |
R |
0.45901265084686 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999974229 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69165a1 |
Quadratic twists by: -3 |