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Hi, I already found out how to generate an elliptic curve in a finite field in sagemath. How to get its oder an element and some more. E.g.

E = EllipticCurve(GF(43),[2,8]);
E.order();                      
E.gens();                       
E.random_element()

But is there a way to check if the EC contains a point with a given x-coordinate?

(which returns a point including the y-coordinate as well)

Or as alternative a function which searches for a point closest to a given x value.

(For small EC I could just search among all elements but target usage is an EC with very high order)

Hi, I already found out how to generate an elliptic curve in a finite field in sagemath. How to get its oder oder, an element and some more. E.g.

E = EllipticCurve(GF(43),[2,8]);
E.order();                      
E.gens();                       
E.random_element()

But is there a way to check if the EC contains a point with a given x-coordinate?

(which returns a point including the y-coordinate as well)

Or as alternative a function which searches for a point closest to a given x value.

(For small EC I could just search among all elements but target usage is an EC with very high order)

Hi, I already found out how to generate an elliptic curve in a finite field in sagemath. How to get its oder, an element and some more. E.g.

E = EllipticCurve(GF(43),[2,8]);
E.order();                      
E.gens();                       
E.random_element()

But is there a way to check if the EC contains a point with a given x-coordinate?

(which returns a point including the y-coordinate as well)

Or as alternative a function which searches for a point closest to a given x value.

(For small EC I could just search among all elements but target usage is an EC with very high order)