Atkin-Lehner |
2+ 3- 5+ 11+ 83- |
Signs for the Atkin-Lehner involutions |
Class |
82170j |
Isogeny class |
Conductor |
82170 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-133687796220 = -1 · 22 · 36 · 5 · 113 · 832 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 0 11+ 2 -2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,750,-15904] |
[a1,a2,a3,a4,a6] |
Generators |
[241:3637:1] |
Generators of the group modulo torsion |
j |
63952011999/183385180 |
j-invariant |
L |
4.7436308080608 |
L(r)(E,1)/r! |
Ω |
0.53298396904396 |
Real period |
R |
4.4500689355192 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001088 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
9130h1 |
Quadratic twists by: -3 |