Atkin-Lehner |
2- 3- 5- 11- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
84150ha |
Isogeny class |
Conductor |
84150 |
Conductor |
∏ cp |
228 |
Product of Tamagawa factors cp |
deg |
612864 |
Modular degree for the optimal curve |
Δ |
-29187587506176000 = -1 · 219 · 39 · 53 · 113 · 17 |
Discriminant |
Eigenvalues |
2- 3- 5- 3 11- 0 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,65110,5148137] |
[a1,a2,a3,a4,a6] |
Generators |
[129:-4025:1] |
Generators of the group modulo torsion |
j |
334992828740851/320302743552 |
j-invariant |
L |
12.051146306373 |
L(r)(E,1)/r! |
Ω |
0.24463812699977 |
Real period |
R |
0.2160575111286 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001093 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
28050bp1 84150dr1 |
Quadratic twists by: -3 5 |