Atkin-Lehner |
2+ 3+ 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368b |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
6594521776128 = 214 · 39 · 112 · 132 |
Discriminant |
Eigenvalues |
2+ 3+ 2 0 11+ 13+ 6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5724,-111888] |
[a1,a2,a3,a4,a6] |
Generators |
[-59:143:1] |
Generators of the group modulo torsion |
j |
64314864/20449 |
j-invariant |
L |
8.3865418561925 |
L(r)(E,1)/r! |
Ω |
0.56264981666886 |
Real period |
R |
1.8631797274212 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997083 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368da2 5148b2 82368j2 |
Quadratic twists by: -4 8 -3 |