Atkin-Lehner |
2+ 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368bx |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
Δ |
6394687782912 = 219 · 38 · 11 · 132 |
Discriminant |
Eigenvalues |
2+ 3- -2 4 11- 13+ 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-67116,6691376] |
[a1,a2,a3,a4,a6] |
Generators |
[109:819:1] |
Generators of the group modulo torsion |
j |
174958262857/33462 |
j-invariant |
L |
6.5062833203609 |
L(r)(E,1)/r! |
Ω |
0.73028869514196 |
Real period |
R |
2.2272983836581 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999987505 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368dt2 2574u2 27456b2 |
Quadratic twists by: -4 8 -3 |