Atkin-Lehner |
2+ 3- 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
51744bo |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
68 |
Product of Tamagawa factors cp |
deg |
221952 |
Modular degree for the optimal curve |
Δ |
-3136192620244992 = -1 · 212 · 317 · 72 · 112 |
Discriminant |
Eigenvalues |
2+ 3- 2 7- 11+ 5 -4 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,23763,-2288133] |
[a1,a2,a3,a4,a6] |
Generators |
[174:2673:1] |
Generators of the group modulo torsion |
j |
7393553366528/15625959723 |
j-invariant |
L |
9.1900076660688 |
L(r)(E,1)/r! |
Ω |
0.23349021337495 |
Real period |
R |
0.57881300293627 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000004 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51744w1 103488gp1 51744d1 |
Quadratic twists by: -4 8 -7 |