Atkin-Lehner |
2+ 3- 7+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
31584j |
Isogeny class |
Conductor |
31584 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
6144 |
Modular degree for the optimal curve |
Δ |
-11938752 = -1 · 26 · 34 · 72 · 47 |
Discriminant |
Eigenvalues |
2+ 3- 0 7+ -6 4 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,42,144] |
[a1,a2,a3,a4,a6] |
Generators |
[0:12:1] |
Generators of the group modulo torsion |
j |
125000000/186543 |
j-invariant |
L |
6.0104334245052 |
L(r)(E,1)/r! |
Ω |
1.5334268206378 |
Real period |
R |
0.97990222676641 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
31584d1 63168cd2 94752z1 |
Quadratic twists by: -4 8 -3 |