Elliptic Function: JE

JE on a Rectangular Torus

rectang elliptic fcn 001
eliptic Riem rectangula 001
eliptic Riem rectangula 001
elliptic je inverse 001
Inverse image of a conformal polar grid on the Riemann sphere under the doubly periodic Jacoby type elliptic function je for a family of rectangular tori. These tori are represented by rectangular fundamental domains for the period translations of je. The je-image of the upper half covers the whole sphere (same for the lower half). The polar centers above each other are preimages of zero (in the middle) and preimages of infinity (at the boundary).

JE on a Rhombic Torus

rombic elliptic fcn 001

JE on a Parallelogram Torus

ellipticJE gauss cart 001
ellipticJE gauss cart 001
celliptic riem parallel 001
celliptic riem parallel 001

z_elliptic_functions.pdf