Atkin-Lehner |
2- 3- 19- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
83448o |
Isogeny class |
Conductor |
83448 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
67584 |
Modular degree for the optimal curve |
Δ |
-16438588416 = -1 · 210 · 36 · 192 · 61 |
Discriminant |
Eigenvalues |
2- 3- -3 -1 -3 1 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5979,178054] |
[a1,a2,a3,a4,a6] |
Generators |
[-82:342:1] [35:108:1] |
Generators of the group modulo torsion |
j |
-31665174628/22021 |
j-invariant |
L |
8.8256315317913 |
L(r)(E,1)/r! |
Ω |
1.2251736666907 |
Real period |
R |
0.90044699085983 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000195 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9272c1 |
Quadratic twists by: -3 |