That curve (which is 11a1) is its own minimal quadratic twist! The
doctstring (E.minimal_quadratic_twst?) says
Determines a quadratic twist with minimal conductor. Returns a
global minimal model of the twist and the fundamental
discriminant
of the quadratic field over which they are isomorphic.
Note: If there is more than one curve with minimal conductor,
the one
returned is the one with smallest label (if in the database),
or
the one with minimal a-invariant list (otherwise).
which looks clear to me (ok, so I wrote it). If you want a different
quadratic twist, use E.quadratic_twist(d), dor example:
sage: E.quadratic_twist(2)
Elliptic Curve defined by y^2 = x^3 + x^2 - 41*x - 199 over Rational
Field
sage: E.quadratic_twist(-1)
Elliptic Curve defined by y^2 = x^3 + x^2 - 165*x + 1427 over Rational
Field
I guess you could argue that E is not a twist of itself, so "minimal
quadratic twist" should mean something different, but this is the
function which was needed by whoever wrote it.
John Cremona
On Jun 15, 8:08 pm, Corinne <[email protected]> wrote:
> When I take an elliptic curve out of Sage's table of elliptic curves
> and then try to use the minimal_quadratic_twist() function, Sage
> returns the original curve as the twist.
>
> Example:
> L=elliptic_curves.rank(0,n=1)
> E=L[0]
> Et, D=E.minimal_quadratic_twist()
>
> Result: E=Et, D=1
>
> How do I ask Sage to give me a new curve?
>
> Corinne
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