Atkin-Lehner |
2+ 3+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
65712c |
Isogeny class |
Conductor |
65712 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
8064 |
Modular degree for the optimal curve |
Δ |
-1051392 = -1 · 28 · 3 · 372 |
Discriminant |
Eigenvalues |
2+ 3+ 2 -3 4 -1 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-12,-48] |
[a1,a2,a3,a4,a6] |
Generators |
[16:60:1] |
Generators of the group modulo torsion |
j |
-592/3 |
j-invariant |
L |
5.0896627678421 |
L(r)(E,1)/r! |
Ω |
1.1492137705955 |
Real period |
R |
2.2144107988566 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000047 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
32856n1 65712e1 |
Quadratic twists by: -4 37 |