Atkin-Lehner |
2+ 3+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368k |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
-15344944902144 = -1 · 212 · 39 · 114 · 13 |
Discriminant |
Eigenvalues |
2+ 3+ 2 2 11- 13- -4 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2484,194400] |
[a1,a2,a3,a4,a6] |
Generators |
[-50:440:1] |
Generators of the group modulo torsion |
j |
-21024576/190333 |
j-invariant |
L |
8.759702069698 |
L(r)(E,1)/r! |
Ω |
0.59786494831635 |
Real period |
R |
1.8314550157956 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003196 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368e2 41184c1 82368g2 |
Quadratic twists by: -4 8 -3 |