Atkin-Lehner |
2+ 3- 5- 11+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
82170w |
Isogeny class |
Conductor |
82170 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1313280 |
Modular degree for the optimal curve |
Δ |
-63862950179635200 = -1 · 218 · 36 · 52 · 115 · 83 |
Discriminant |
Eigenvalues |
2+ 3- 5- -3 11+ -7 2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,67536,-10126080] |
[a1,a2,a3,a4,a6] |
Generators |
[480:11280:1] |
Generators of the group modulo torsion |
j |
46730300206447871/87603498188800 |
j-invariant |
L |
3.3013621746296 |
L(r)(E,1)/r! |
Ω |
0.18269062966051 |
Real period |
R |
2.2588475022342 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999839695 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9130g1 |
Quadratic twists by: -3 |