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2020-10-12 15:32:53 +0200 commented answer How is curve C(b) converted to elliptic curve?

Thank you very much for your answer, but it gives an error after the "WeierstrassForm(cubic)" command, it does not calculate. I do not understand why it gives an error.

2020-10-12 15:32:03 +0200 answered a question How is curve C(b) converted to elliptic curve?

Thank you very much for your answer, but it gives an error after the "WeierstrassForm(cubic)" command, it does not calculate. I do not understand why it gives an error.

2020-10-12 14:57:38 +0200 asked a question How is curve C(b) converted to elliptic curve?

How can we transform curve $$ C(b)\ :\ (3+b)X^2Y + (9+b)XY^2 - (4+b)X^2Z + (3-b^2)XYZ + (-4+b)Y^2Z + (-9+b)XZ^2+bYZ^2 $$ into an elliptic curve without valuing $b$?

Edited: Expression in code format:

(3+b)*X^2*Y + (9+b)*X*Y^2 - (4+b)*X^2*Z + (3-b^2)*X*Y*Z + (-4+b)*Y^2*Z + (-9+b)*X*Z^2 + b*Y*Z^2
2020-08-05 11:36:20 +0200 asked a question How to find the generator of the points on the quartic curve?

How to find the generator of the points on a quartic curve?

For example, given the curve

y^2 = -2500*x^4 + 451976*x^2 - 2500

how do I find the generator of the points on that curve?

2020-05-14 11:23:13 +0200 received badge  Supporter (source)
2020-05-14 11:16:32 +0200 asked a question How do I convert a 6th degree curve to an elliptic curve?

How do I convert a 6th degree curve to an elliptic curve?

exp: How does y^2=16x^6-32x^5+272x^4+4096x^2-8192*x+69632 curve convert to elliptic curve?

Thanks.

2020-05-11 13:27:33 +0200 received badge  Editor (source)
2020-05-11 11:03:47 +0200 asked a question How can I find the points on the hyperelliptic curve?

How can I find points on a hyperelliptic curve?

For example, consider the curve defined by the equation $$ y^2 =2000 x^6 + 8000 x^5 + 27625 x^4 + 70500 x^3 + 345750 x^2 + 62500 x + 1968750 $$

How can I find points on that curve?

2020-03-26 18:32:21 +0200 commented answer What is the point 𝑃1=(βˆ’1,3) on the y^2=7π‘₯4+π‘₯3+π‘₯2+π‘₯+3 curve and the point corresponding to P on the x^2=x^3βˆ’250/3xβˆ’124927 curve?

sage: P2.<x,y,z> = ProjectiveSpace(QQ,2)

sage: E1= Curve(y^2z^2+15x^4-1516z^4)

sage: phi = Jacobian(E1, morphism=True)

sage: E2 = phi.codomain(); E2

Elliptic Curve defined by y^2 = x^3 + 14400*x over Rational Field

sage: phi(E1(2,0,1))

(0 : 1 : 0)

But the (0 : 1 : 0) point is not on the E2 curve. What should I do?

2020-03-26 18:23:23 +0200 received badge  Scholar (source)
2020-03-26 18:17:58 +0200 answered a question What is the point 𝑃1=(βˆ’1,3) on the y^2=7π‘₯4+π‘₯3+π‘₯2+π‘₯+3 curve and the point corresponding to P on the x^2=x^3βˆ’250/3xβˆ’124927 curve?

sage: P2.<x,y,z> = ProjectiveSpace(QQ,2) sage: E1= Curve(y^2z^2+15x^4-1516z^4) sage: phi = Jacobian(E1, morphism=True) sage: E2 = phi.codomain(); E2 Elliptic Curve defined by y^2 = x^3 + 14400*x over Rational Field sage: phi(E1(2,0,1)) (0 : 1 : 0)

But the (0 : 1 : 0) point is not on the E2 curve. What should I do?

2020-03-26 16:35:23 +0200 received badge  Student (source)
2020-03-26 16:08:06 +0200 asked a question What is the point 𝑃1=(βˆ’1,3) on the y^2=7π‘₯4+π‘₯3+π‘₯2+π‘₯+3 curve and the point corresponding to P on the x^2=x^3βˆ’250/3xβˆ’124927 curve?

What is the point 𝑃1=(βˆ’1,3) on the y^2=7π‘₯^4+π‘₯^3+π‘₯^2+π‘₯+3 curve and the point corresponding to P on the x^2=x^3βˆ’250/3xβˆ’124927 curve? (𝐸1:𝑦2=7π‘₯4+π‘₯3+π‘₯2+π‘₯+3,𝑃1=(βˆ’1,3) can be transformed to 𝐸2:𝑣2=𝑒3βˆ’250𝑒3βˆ’124927) Thanks

2020-03-22 17:05:01 +0200 asked a question I have the hyperelliptic curve y^2=x^4+81473/1024*x^2-1. How do I convert this curve to an elliptic curve in a short weierstrass form?

I have the hyperelliptic curve $y^2=x^4+81473/1024x^2-1$. How do I convert this curve to an elliptic curve in a short Weierstrass form? Also, how can I convert the point $(x,y,z)=(1,i,0)$ on the $y^2=x^4+81473/1024x^2z^2- z^4$ curve to the point on the elliptic curve? Thanks.