>From the example you give:
2x**3+385x**2+256x-58195=3y**2 , over the rational field
it's not direct because sage does not handle general cubic equation
yet.
In sage, let's define:
{{{
sage: R.<x,y> = QQ[]
sage: P = 2*x**3 + 385*x**2 + 256*x - 58195 - 3*y**2
}}}
Given an equation
A6 + A4 x + A3 y + A2 x**2 + A1 xy + A5 y**2 + A7 x**3 = 0.
You can obtain do by hand the change of variables Q(x' , y' ) = P( -
x*A5*A7 , y * A7**2 * A5 ) / ( A5**3 * A7**4 )
a simplified equation:
{{{
sage: Q = P( x=-x*(-3)*2 , y=y*2**2*(-3) ) / ( (-3)**3*2**4 )
sage: Q
-x^3 - 385/12*x^2 + y^2 - 32/9*x + 58195/432
}}}
You can then define the elliptic curve and compute integral points
{{{
sage: E = EllipticCurve(Q)
sage: time pts = E.integral_model().integral_points()
CPU times: user 2.74 s, sys: 0.02 s, total: 2.76 s
Wall time: 7.58 s
}}}
at this point, you need to come back to the original curve, removing
solutions not integral after the inverse change of variables
{{{
sage: x_coords = [ x/6 for x,y,z in pts if 6.divides(ZZ(x)) ]
sage: x_coords
[-191, -157, -67, -49, -23, -19, 19, 23, 61, 103, 521, 817, 3857,
10687, 276251]
}}}
On Dec 6, 6:41 pm, Jaakko Seppälä <jaakko.j.sepp...@gmail.com> wrote:
> I read
> fromhttp://mathoverflow.net/questions/7907/elliptic-curves-integer-points
> than Sage can determine the integer points of an elliptic curve. What
> commands will do the trick?
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