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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 $(u,r,s,t) = (1, -1/3, 0, 0)$.

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 $(u,r,s,t) = (1, -1/3, 0, 0)$.

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 $(u,r,s,t) = (1, -1/3, 0, 0)$.

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 $(u,r,s,t) = (1, -1/3, 0, 0)$.

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 $(u,r,s,t) = (1, -1/3, 0, 0)$.

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:

What is wrong with the page? My question looks OK in preview window, but when sent there is gibberish onside inside $$.

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 $(u,r,s,t) = (1, -1/3, 0, 0)$.

EDIT:

What is wrong with the page? My question looks OK in preview window, but when sent there is gibberish inside $$.

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 $(u,r,s,t) = (1, -1/3, 0, 0)$.

EDIT:

What is wrong with the page? My question looks OK in preview window, but when sent there is gibberish inside $$.

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 $$.

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 $$.

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 $$.

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

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 looks OK in preview window, but when sent there is gibberish inside $$.

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 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 $$.

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 looks looked OK in preview window, but when sent there is was gibberish inside $$.

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 $$.