Atkin-Lehner |
2- 11- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
4048j |
Isogeny class |
Conductor |
4048 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
864 |
Modular degree for the optimal curve |
Δ |
-23555312 = -1 · 24 · 112 · 233 |
Discriminant |
Eigenvalues |
2- -1 0 4 11- 5 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,22,223] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:11:1] |
Generators of the group modulo torsion |
j |
70304000/1472207 |
j-invariant |
L |
3.4102660129424 |
L(r)(E,1)/r! |
Ω |
1.5960010547134 |
Real period |
R |
1.0683783707006 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
1012b1 16192q1 36432bs1 101200bw1 |
Quadratic twists by: -4 8 -3 5 |