Different algorithms for has_rational_point return different answers.

edit

There seems to be an inconsistency.

Define a polynomial ring in three variables:

sage: R.<x, y, z> = QQ[]

Define a conic:

sage: C = Conic(27628*(x^2 - y^2) - 81746*x*y  - z^2)

Check whether the conic has rational points, using algorithm="local":

sage: C.has_rational_point(algorithm="local", obstruction=True)
(True, None)

Check whether the conic has rational points, using algorithm="default":

sage: C.has_rational_point(algorithm="default", obstruction=True)
(False, 17)