Atkin-Lehner |
2+ 3- 5- 11- 83- |
Signs for the Atkin-Lehner involutions |
Class |
82170bb |
Isogeny class |
Conductor |
82170 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
230400 |
Modular degree for the optimal curve |
Δ |
4043380275000 = 23 · 311 · 55 · 11 · 83 |
Discriminant |
Eigenvalues |
2+ 3- 5- 2 11- 3 -8 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-19089,-1005755] |
[a1,a2,a3,a4,a6] |
Generators |
[-79:107:1] |
Generators of the group modulo torsion |
j |
1055257664218129/5546475000 |
j-invariant |
L |
5.8434919899001 |
L(r)(E,1)/r! |
Ω |
0.40629372210085 |
Real period |
R |
1.4382432387084 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004258 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27390n1 |
Quadratic twists by: -3 |