Atkin-Lehner |
2+ 3- 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
51744bl |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
16384 |
Modular degree for the optimal curve |
Δ |
-215151552 = -1 · 26 · 34 · 73 · 112 |
Discriminant |
Eigenvalues |
2+ 3- 2 7- 11+ 0 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,138,-288] |
[a1,a2,a3,a4,a6] |
Generators |
[9:42:1] |
Generators of the group modulo torsion |
j |
13144256/9801 |
j-invariant |
L |
8.4876919071501 |
L(r)(E,1)/r! |
Ω |
0.99360038894841 |
Real period |
R |
1.0677949608277 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999829 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
51744r1 103488gk1 51744j1 |
Quadratic twists by: -4 8 -7 |