Atkin-Lehner |
2- 3+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368db |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
61440 |
Modular degree for the optimal curve |
Δ |
-126817726464 = -1 · 212 · 39 · 112 · 13 |
Discriminant |
Eigenvalues |
2- 3+ 2 -2 11- 13+ -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-324,17280] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:135:1] |
Generators of the group modulo torsion |
j |
-46656/1573 |
j-invariant |
L |
7.2242434309899 |
L(r)(E,1)/r! |
Ω |
0.86964542225304 |
Real period |
R |
2.0767784340384 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999975201 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368cq1 41184t1 82368cs1 |
Quadratic twists by: -4 8 -3 |