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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: |
| 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 how do I find the generator of the points on that curve? |
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| 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. |
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| 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 π1=(β1,3) on the y^2=7π₯4+π₯3+π₯2+π₯+3 curve and the point corresponding to P on the x^2=x^3β250/3xβ124927 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? |
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| 2020-03-26 18:17:58 +0200 | answered a question | What is the point π1=(β1,3) on the y^2=7π₯4+π₯3+π₯2+π₯+3 curve and the point corresponding to P on the x^2=x^3β250/3xβ124927 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? |
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| 2020-03-26 16:08:06 +0200 | asked a question | What is the point π1=(β1,3) on the y^2=7π₯4+π₯3+π₯2+π₯+3 curve and the point corresponding to P on the x^2=x^3β250/3xβ124927 curve? What is the point π1=(β1,3) on the y^2=7π₯^4+π₯^3+π₯^2+π₯+3 curve and the point corresponding to P on the x^2=x^3β250/3xβ124927 curve? (πΈ1:π¦2=7π₯4+π₯3+π₯2+π₯+3,π1=(β1,3) can be transformed to πΈ2:π£2=π’3β250π’3β124927) 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. |
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