# Different algorithms for has_rational_point return different answers.

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)
```