How do you compute the
-invariant of an elliptic curve
in Sage?
Other methods associated to the EllipticCurve class are
j_invariant
, discriminant
, and
weierstrass_model
. Here is an example of their syntax.
sage: E = EllipticCurve([0, -1, 1, -10, -20]) sage: E Elliptic Curve defined by y^2 + y = x^3 - x^2 - 10*x - 20 over Rational Field sage: E.j_invariant() -122023936/161051 sage: E.short_weierstrass_model() Elliptic Curve defined by y^2 = x^3 - 13392*x - 1080432 over Rational Field sage: E.discriminant() -161051 sage: E = EllipticCurve(GF(5),[0, -1, 1, -10, -20]) sage: E.short_weierstrass_model() Elliptic Curve defined by y^2 = x^3 + 3*x + 3 over Finite Field of size 5 sage: E.j_invariant() 4
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