ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 26 Dec 2019 16:41:15 +0100How to convert output of 'isomorphism_to' to transformation rulehttps://ask.sagemath.org/question/49149/how-to-convert-output-of-isomorphism_to-to-transformation-rule/Input:
C = EllipticCurve([0,0,0,-((250)/3),-(1249/27)])
print(C)
Cmin=C.minimal_model()
print(Cmin)
Cmin.isomorphism_to(C)
Output:
Elliptic Curve defined by y^2 = x^3 - 250/3*x - 1249/27 over Rational Field
Elliptic Curve defined by y^2 = x^3 + x^2 - 83*x - 74 over Rational Field
Generic morphism:
From: Abelian group of points on Elliptic Curve defined by y^2 = x^3 + x^2 - 83*x - 74 over Rational Field
To: Abelian group of points on Elliptic Curve defined by y^2 = x^3 - 250/3*x - 1249/27 over Rational Field
Via: (u,r,s,t) = (1, -1/3, 0, 0)
But I want explicit transformation like $(x,y) = (u^2 x+r , u^3 y + s u^2 x + t)$, in our case it would be $(x, y) = (-(1/3) + x, y)$ instead of just showing $(u,r,s,t) = (1, -1/3, 0, 0)$.
EDIT:
What is wrong with the page? My question looked OK in preview window, but when sent there was gibberish inside $$.Mon, 23 Dec 2019 22:21:21 +0100https://ask.sagemath.org/question/49149/how-to-convert-output-of-isomorphism_to-to-transformation-rule/Answer by azerbajdzan for <p>Input:</p>
<pre><code>C = EllipticCurve([0,0,0,-((250)/3),-(1249/27)])
print(C)
Cmin=C.minimal_model()
print(Cmin)
Cmin.isomorphism_to(C)
</code></pre>
<p>Output:</p>
<pre><code>Elliptic Curve defined by y^2 = x^3 - 250/3*x - 1249/27 over Rational Field
Elliptic Curve defined by y^2 = x^3 + x^2 - 83*x - 74 over Rational Field
Generic morphism:
From: Abelian group of points on Elliptic Curve defined by y^2 = x^3 + x^2 - 83*x - 74 over Rational Field
To: Abelian group of points on Elliptic Curve defined by y^2 = x^3 - 250/3*x - 1249/27 over Rational Field
Via: (u,r,s,t) = (1, -1/3, 0, 0)
</code></pre>
<p>But I want explicit transformation like $(x,y) = (u^2 x+r , u^3 y + s u^2 x + t)$, in our case it would be $(x, y) = (-(1/3) + x, y)$ instead of just showing $(u,r,s,t) = (1, -1/3, 0, 0)$.</p>
<p>EDIT:</p>
<p>What is wrong with the page? My question looked OK in preview window, but when sent there was gibberish inside $$.</p>
https://ask.sagemath.org/question/49149/how-to-convert-output-of-isomorphism_to-to-transformation-rule/?answer=49210#post-id-49210Input:
from sage.schemes.elliptic_curves.weierstrass_morphism import *
C = EllipticCurve([0,0,0,-((250)/3),-(1249/27)])
print(C)
Cmin=C.minimal_model()
print(Cmin)
(u,r,s,t)=isomorphisms(Cmin,C,True)
var('x y')
[u^2*x+r,u^3*y+s*u^2*x+t]
Output:
Elliptic Curve defined by y^2 = x^3 - 250/3*x - 1249/27 over Rational Field
Elliptic Curve defined by y^2 = x^3 + x^2 - 83*x - 74 over Rational Field
[x - 1/3, y]Thu, 26 Dec 2019 16:41:15 +0100https://ask.sagemath.org/question/49149/how-to-convert-output-of-isomorphism_to-to-transformation-rule/?answer=49210#post-id-49210