Atkin-Lehner |
2+ 3- 5+ 11+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
84150bf |
Isogeny class |
Conductor |
84150 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
2211840 |
Modular degree for the optimal curve |
Δ |
11830067339062500 = 22 · 39 · 58 · 113 · 172 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -2 11+ 4 17+ 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-4213917,-3328427759] |
[a1,a2,a3,a4,a6] |
j |
726497538898787209/1038579300 |
j-invariant |
L |
0.84298145067537 |
L(r)(E,1)/r! |
Ω |
0.10537269624606 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
28050cj1 16830cp1 |
Quadratic twists by: -3 5 |