Atkin-Lehner |
2- 3- 11- 37- |
Signs for the Atkin-Lehner involutions |
Class |
39072r |
Isogeny class |
Conductor |
39072 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
12544 |
Modular degree for the optimal curve |
Δ |
-16879104 = -1 · 29 · 34 · 11 · 37 |
Discriminant |
Eigenvalues |
2- 3- 3 -4 11- 0 -3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-144,648] |
[a1,a2,a3,a4,a6] |
Generators |
[6:-6:1] |
Generators of the group modulo torsion |
j |
-649461896/32967 |
j-invariant |
L |
7.7051872956334 |
L(r)(E,1)/r! |
Ω |
2.1693324958895 |
Real period |
R |
0.44398376633345 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999961 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
39072l1 78144bu1 117216k1 |
Quadratic twists by: -4 8 -3 |