Atkin-Lehner |
2+ 3+ 5+ 11- 83- |
Signs for the Atkin-Lehner involutions |
Class |
82170c |
Isogeny class |
Conductor |
82170 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
518400 |
Modular degree for the optimal curve |
Δ |
82193237676000 = 25 · 33 · 53 · 113 · 833 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ -4 11- -1 0 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-117660,15557616] |
[a1,a2,a3,a4,a6] |
Generators |
[-90:32913:8] |
Generators of the group modulo torsion |
j |
6671885067421427547/3044193988000 |
j-invariant |
L |
2.3669011207714 |
L(r)(E,1)/r! |
Ω |
0.59899363859681 |
Real period |
R |
1.9757314331667 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002899 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
82170bk2 |
Quadratic twists by: -3 |