Atkin-Lehner |
2+ 3+ 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
51744n |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
61440 |
Modular degree for the optimal curve |
Δ |
-57397652928 = -1 · 26 · 32 · 77 · 112 |
Discriminant |
Eigenvalues |
2+ 3+ -4 7- 11+ -6 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,670,-9624] |
[a1,a2,a3,a4,a6] |
Generators |
[14:48:1] [19:98:1] |
Generators of the group modulo torsion |
j |
4410944/7623 |
j-invariant |
L |
6.1164315009355 |
L(r)(E,1)/r! |
Ω |
0.58531194563478 |
Real period |
R |
1.3062332715379 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
51744ct1 103488em1 7392d1 |
Quadratic twists by: -4 8 -7 |