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Full-Text Articles in Number Theory
Elliptic Curves Of High Rank, Cecylia Bocovich
Elliptic Curves Of High Rank, Cecylia Bocovich
Mathematics, Statistics, and Computer Science Honors Projects
The study of elliptic curves grows out of the study of elliptic functions which dates back to work done by mathematicians such as Weierstrass, Abel, and Jacobi. Elliptic curves continue to play a prominent role in mathematics today. An elliptic curve E is defined by the equation, y2 = x3 + ax + b, where a and b are coefficients that satisfy the property 4a3 + 27b2 = 0. The rational solutions of this curve form a group. This group, denoted E(Q), is known as the Mordell-Weil group and was proved by Mordell to be isomorphic …