toWeierstrass -- A method to transform a smooth plane cubic into Weierstrass form.

Synopsis

• Usage:

  toWeierstrass(List,List,Thing)

• Inputs:
  • L, the coefficients of a plane cubic.
  • O, the coordinates of a point over the curve.
  • K, any field
• Outputs:
  • an instance of the type EllipticCurve

Description

The method use the a modified version Nagell's algorithm which works in any characteristic.

Reference: Tibouchi, M. ''A Nagell Algorithm in Any Characteristic'', Cryptography and Security: From Theory to Applications, 474--479, 2012.

i1 : toWeierstrass({-1,0,+1,0,0,+1,0,-1,0,+2},{1,2,1},ZZ/13)
The point is not on the curve