Atkin-Lehner |
2- 3- 5- 11- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
82170cb |
Isogeny class |
Conductor |
82170 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
483840 |
Modular degree for the optimal curve |
Δ |
-4044523742941770 = -1 · 2 · 312 · 5 · 113 · 833 |
Discriminant |
Eigenvalues |
2- 3- 5- 2 11- -1 -3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,39433,517529] |
[a1,a2,a3,a4,a6] |
Generators |
[92190:2173777:1000] |
Generators of the group modulo torsion |
j |
9302206264310231/5548043543130 |
j-invariant |
L |
12.013919759211 |
L(r)(E,1)/r! |
Ω |
0.2686004405164 |
Real period |
R |
7.454641383795 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001445 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27390e1 |
Quadratic twists by: -3 |