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WeierstrassInvariants

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Invariants {g2 g3} of the Weierstrass elliptic function for a lattice given by its half-periods (numeric via theta constants; exact closed forms for the square and hexagonal CM lattices)

WeierstrassInvariants[{ω 1, ω 3}]
WeierstrassInvariants[{1., 2.I}] → {8.124218443053024 + 0.*I, 4.443052044945954 + 0.*I}WeierstrassP[2.6, WeierstrassInvariants[{1.5, 1 - I}]] → WeierstrassP[2.6, {-1.675848543687281 + 4.365388350313803*I, 2.469412539535981 - 1.3011730452487709*I}]Plot[Im[WeierstrassInvariants[{ω1, 1 + I}]], {ω1, -2, 2}] → -Graphics-
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WeierstrassPInverseWeierstrassPKleinInvariantJWeierstrassInvariantG2WeierstrassInvariantG3WeierstrassHalfPeriodsEllipticExpEllipticLogEllipticNomeQInverseEllipticNomeQJacobiAmplitude

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