Atkin-Lehner |
5+ 7+ 11+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
82775d |
Isogeny class |
Conductor |
82775 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1376640 |
Modular degree for the optimal curve |
Δ |
-557021849248046875 = -1 · 510 · 72 · 114 · 433 |
Discriminant |
Eigenvalues |
-2 2 5+ 7+ 11+ 2 1 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-78958,-36883432] |
[a1,a2,a3,a4,a6] |
Generators |
[2585715:63295046:3375] |
Generators of the group modulo torsion |
j |
-5574649753600/57039037363 |
j-invariant |
L |
4.4331972505351 |
L(r)(E,1)/r! |
Ω |
0.12376216492631 |
Real period |
R |
8.9550737287591 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000008011 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82775bc1 |
Quadratic twists by: 5 |