Atkin-Lehner |
2- 3- 7+ 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
48048bz |
Isogeny class |
Conductor |
48048 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
16128 |
Modular degree for the optimal curve |
Δ |
-405909504 = -1 · 212 · 32 · 7 · 112 · 13 |
Discriminant |
Eigenvalues |
2- 3- -1 7+ 11+ 13+ -4 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-21,963] |
[a1,a2,a3,a4,a6] |
Generators |
[6:33:1] |
Generators of the group modulo torsion |
j |
-262144/99099 |
j-invariant |
L |
5.8266956114031 |
L(r)(E,1)/r! |
Ω |
1.3669765034994 |
Real period |
R |
1.0656173673226 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999994 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
3003g1 |
Quadratic twists by: -4 |