Skip to content# Elliptic Curves

### Elliptic curves with complex multiplication give rise to tori over the complex numbers

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### Summary

— mathematics, 3d printing, autodesk maya — 1 min read

Completed in spring 2016 at the Mathematical Computing Laboratory at UIC.

This repository contains the paper, poster, images, and 3d modeling files from my research and learning project on elliptic curves. I completed this project with James Duncan under the guidance of Cara Mullen (PhD) and Professor Alina Cojocaru (PhD).

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Our research focuses on elliptic curves $E over $Q with complex multiplication (by the maximal order of an imaginary quadratic field). Viewed over $C, each $E gives rise to two tori, defined by the generators $\omega_1 and $\omega_2 of the period lattice. These tori can be constructed virtually into a 3D mesh. Further, this mesh can be translated into gcode and printed using a 3D printer.