Atkin-Lehner |
2+ 3- 5- 11- 83- |
Signs for the Atkin-Lehner involutions |
Class |
82170z |
Isogeny class |
Conductor |
82170 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
700416 |
Modular degree for the optimal curve |
Δ |
-36220406421196800 = -1 · 212 · 318 · 52 · 11 · 83 |
Discriminant |
Eigenvalues |
2+ 3- 5- -1 11- -1 0 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,81666,1755540] |
[a1,a2,a3,a4,a6] |
Generators |
[204:5082:1] |
Generators of the group modulo torsion |
j |
82626060291589151/49685056819200 |
j-invariant |
L |
5.1425349720667 |
L(r)(E,1)/r! |
Ω |
0.22441375417547 |
Real period |
R |
2.864427244772 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999991688 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27390w1 |
Quadratic twists by: -3 |