algcurves[j_invariant] - The j invariant of an elliptic curve
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Calling Sequence
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j_invariant(f, x, y)
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Parameters
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f
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polynomial in x and y representing a curve of genus 1
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x, y
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variables
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Description
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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.
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The curve must be irreducible and have genus 1, otherwise the j invariant is not defined and this procedure will fail.
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Examples
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Check that the genus is 1, because only then is the j invariant defined.
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