ellCurve(List,Thing) -- A method for creating elliptic curves in Weierstrass form.

Synopsis

• Function: ellCurve

• Usage:

  ellCurve(L,K)

• Inputs:
  • L, a list of five coefficients in the field K
  • K, any field
• Outputs:
  • an instance of the type EllipticCurveW

Description

Returns an elliptic curve in Weierstrass with coefficients from the list.

i1 : ellCurve({1,2,3,4,6},GF(29))

o1 = Elliptic Curve defined by Y^2 + 1 XY + 3 Y = X^3 + 2 X^2 + 4 X + 6( over(GF 29 .))

o1 : EllipticCurveW

i2 : ellCurve({0,-1,1,-10,-20},QQ)

o2 = Elliptic Curve defined by Y^2 + 0 XY + 1 Y = X^3 + (-1)X^2 + (-10)X + (-20)( over(QQ .))

o2 : EllipticCurveW