Atkin-Lehner |
2- 3- 7- 13- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
82992cq |
Isogeny class |
Conductor |
82992 |
Conductor |
∏ cp |
15 |
Product of Tamagawa factors cp |
deg |
182400 |
Modular degree for the optimal curve |
Δ |
-5461250715648 = -1 · 212 · 33 · 7 · 135 · 19 |
Discriminant |
Eigenvalues |
2- 3- -2 7- 3 13- 6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-9989,-403725] |
[a1,a2,a3,a4,a6] |
Generators |
[118:273:1] |
Generators of the group modulo torsion |
j |
-26913692127232/1333313163 |
j-invariant |
L |
8.5330323253976 |
L(r)(E,1)/r! |
Ω |
0.23808563947885 |
Real period |
R |
2.3893453754561 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000736 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5187a1 |
Quadratic twists by: -4 |