Atkin-Lehner |
2- 3+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368dh |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
Δ |
1120833506377728 = 224 · 33 · 114 · 132 |
Discriminant |
Eigenvalues |
2- 3+ 2 2 11- 13- -8 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-959512524,11439948916112] |
[a1,a2,a3,a4,a6] |
j |
13802951728468271053322091/158357056 |
j-invariant |
L |
2.6944161843129 |
L(r)(E,1)/r! |
Ω |
0.16840101156593 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368f2 20592r2 82368cx2 |
Quadratic twists by: -4 8 -3 |