# Revision history [back]

### 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 $(x,y) = (u^2x+r , u^3y + su^2x + t)$, in our case it would be $(x, y) = (-(1/3) + x, y)$ instead of just showing $(u,r,s,t) = (1, -1/3, 0, 0)$.

### 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 $(x,y) = (u^2x+r , u^3y + su^2x + t)$, in our case it would be $(x, y) = (-(1/3) + x, y)$ instead of just showing $(u,r,s,t) = (1, -1/3, 0, 0)$.

### 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 $(x,y) '(x,y) = (u^2x+r , u^3y + su^2x + t)$, t)', in our case it would be $(x, y) = (-(1/3) + x, y)$ instead of just showing $(u,r,s,t) = (1, -1/3, 0, 0)$.

### 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) $(x,y) = (u^2x+r , u^3y + su^2x + t)', t)$, in our case it would be $(x, y) = (-(1/3) + x, y)$ instead of just showing $(u,r,s,t) = (1, -1/3, 0, 0)$.

### 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 $(x,y) = (u^2x+r , u^3y + su^2x + t)$, 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:

### 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)


### 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 $(x,y) = (u^2x+r , u^3y + su^2x + t)$, 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 looks OK in preview window, but when sent there is gibberish inside $$. ### How to convert output of 'isomorphism_to' to transformation rule Input: C = EllipticCurve([0,0,0,-((250)/3),-(1249/27)]) print(C) Cmin=C.minimal_model() print(Cmin) Cmin.isomorphism_to(C)  Output: Elliptic Curve defined by y^2 = x^3 - 250/3*x - 1249/27 over Rational Field Elliptic Curve defined by y^2 = x^3 + x^2 - 83*x - 74 over Rational Field Generic morphism: From: Abelian group of points on Elliptic Curve defined by y^2 = x^3 + x^2 - 83*x - 74 over Rational Field To: Abelian group of points on Elliptic Curve defined by y^2 = x^3 - 250/3*x - 1249/27 over Rational Field Via: (u,r,s,t) = (1, -1/3, 0, 0)  But I want explicit transformation like (x,y) = (u^2x+r , u^3y + su^2x + t) in t). In our case it would be (x, y) = (-(1/3) + x, y) instead of just showing (u,r,s,t) = (1, -1/3, 0, 0). EDIT: What is wrong with the page? My question looks OK in preview window, but when sent there is gibberish inside$$. ### 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$(x,y) = (u^2x+r , u^3y + su^2x + t)$. 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:

### 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 $(x,y) = (u^2 x+r , u^3 y + s u^2 x + t)$.