The j invariant of an elliptic curve
j_invariant(f, x, y)
polynomial in x and y representing a curve of genus 1
For algebraic curves with genus 1 one can compute a number called the j invariant. An important property of this j invariant is the following: two elliptic (i.e. genus = 1) curves are birationally equivalent (i.e. can be transformed to each other with rational transformations over an algebraically closed field of constants) if and only if their j invariants are the same.
The curve must be irreducible and have genus 1, otherwise the j invariant is not defined and this procedure will fail.
f ≔ y5+43−23⁢y23+11⁢y3−17⁢y43−16⁢x23+16⁢x33−4⁢x43:
Check that the genus is 1, because only then is the j invariant defined.
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