Atkin-Lehner |
2- 3+ 19+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
81168bn |
Isogeny class |
Conductor |
81168 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
76800 |
Modular degree for the optimal curve |
Δ |
-721523780352 = -1 · 28 · 35 · 194 · 89 |
Discriminant |
Eigenvalues |
2- 3+ 0 2 -2 -2 4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-3493,-88199] |
[a1,a2,a3,a4,a6] |
Generators |
[3437:201438:1] |
Generators of the group modulo torsion |
j |
-18416361472000/2818452267 |
j-invariant |
L |
5.5603729809265 |
L(r)(E,1)/r! |
Ω |
0.30790016178598 |
Real period |
R |
4.5147532139819 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001603 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
20292j1 |
Quadratic twists by: -4 |