Atkin-Lehner |
2+ 3+ 11- 29- |
Signs for the Atkin-Lehner involutions |
Class |
84216f |
Isogeny class |
Conductor |
84216 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
1008000 |
Modular degree for the optimal curve |
Δ |
-21502369994029056 = -1 · 211 · 35 · 116 · 293 |
Discriminant |
Eigenvalues |
2+ 3+ 1 3 11- -4 -5 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-716360,-233238036] |
[a1,a2,a3,a4,a6] |
Generators |
[704177434:94145301503:39304] |
Generators of the group modulo torsion |
j |
-11205525764162/5926527 |
j-invariant |
L |
6.0209050314962 |
L(r)(E,1)/r! |
Ω |
0.082048925775844 |
Real period |
R |
12.230314560283 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000343 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
696d1 |
Quadratic twists by: -11 |