Atkin-Lehner |
2- 3+ 13+ 83- |
Signs for the Atkin-Lehner involutions |
Class |
84162n |
Isogeny class |
Conductor |
84162 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
2935296 |
Modular degree for the optimal curve |
Δ |
-4080279092030199396 = -1 · 22 · 37 · 138 · 833 |
Discriminant |
Eigenvalues |
2- 3+ 1 2 1 13+ 2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-8629735,-9761708767] |
[a1,a2,a3,a4,a6] |
Generators |
[269553626322291:60895896040446920:5240822553] |
Generators of the group modulo torsion |
j |
-14725022956601670649/845336762244 |
j-invariant |
L |
10.539947432093 |
L(r)(E,1)/r! |
Ω |
0.044042168887013 |
Real period |
R |
19.942908691161 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6474d1 |
Quadratic twists by: 13 |