Atkin-Lehner |
2+ 3- 7- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
9744f |
Isogeny class |
Conductor |
9744 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
2048 |
Modular degree for the optimal curve |
Δ |
-1091328 = -1 · 28 · 3 · 72 · 29 |
Discriminant |
Eigenvalues |
2+ 3- -4 7- 4 2 -2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,20,44] |
[a1,a2,a3,a4,a6] |
Generators |
[7:24:1] |
Generators of the group modulo torsion |
j |
3286064/4263 |
j-invariant |
L |
4.3820869474196 |
L(r)(E,1)/r! |
Ω |
1.8541178334759 |
Real period |
R |
2.3634349814782 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4872c1 38976bn1 29232p1 68208i1 |
Quadratic twists by: -4 8 -3 -7 |