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WeierstrassInvariants

  • WeierstrassInvariants[ , ] gives the invariants , for Weierstrass elliptic functions corresponding to the half-periods , .
  • Mathematical function (see Section A.3.10).
  • WeierstrassInvariants is the inverse of WeierstrassHalfPeriods.
  • See the Mathematica book: Section 3.2.11.
  • See also: WeierstrassP, InverseWeierstrassP, KleinInvariantJ.

    Further Examples

    From two complex numbers and that are not linearly dependent over the reals, we can form the two Weierstrass invariants and , where both sums are over the nonzero elements of the lattice generated by and . The quotient of the complex plane by this lattice is equivalent, as a complex curve, to the elliptic curve with equation .
    WeierstrassInvariants returns and , given and .

    In[1]:=

    Out[1]=

    The Weierstrass invariants depend only on the lattice, not on the particular generators.

    In[2]:=

    Out[2]=