Atkin-Lehner |
2+ 3+ 11+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
48576f |
Isogeny class |
Conductor |
48576 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
119808 |
Modular degree for the optimal curve |
Δ |
-2297902058496 = -1 · 210 · 36 · 11 · 234 |
Discriminant |
Eigenvalues |
2+ 3+ -2 2 11+ -6 4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-19029,1019349] |
[a1,a2,a3,a4,a6] |
Generators |
[84:81:1] |
Generators of the group modulo torsion |
j |
-744208243621888/2244044979 |
j-invariant |
L |
3.4947059182348 |
L(r)(E,1)/r! |
Ω |
0.82237288262055 |
Real period |
R |
2.1247696708614 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999218 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
48576dy1 3036g1 |
Quadratic twists by: -4 8 |