Atkin-Lehner |
2- 3- 5- 11- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
82170bz |
Isogeny class |
Conductor |
82170 |
Conductor |
∏ cp |
350 |
Product of Tamagawa factors cp |
deg |
1260000 |
Modular degree for the optimal curve |
Δ |
-323524466852400000 = -1 · 27 · 36 · 55 · 115 · 832 |
Discriminant |
Eigenvalues |
2- 3- 5- 1 11- -6 -1 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-81977,28839129] |
[a1,a2,a3,a4,a6] |
Generators |
[117:4506:1] |
Generators of the group modulo torsion |
j |
-83573247837920329/443792135600000 |
j-invariant |
L |
11.913510001752 |
L(r)(E,1)/r! |
Ω |
0.2641735418298 |
Real period |
R |
0.12884939106018 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000177 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9130a1 |
Quadratic twists by: -3 |