Number Theory


A Brief Investigation Into Two Sets of Elliptic Curves

Authors: Lulu Karami

This submission is more or less an amateur exposition on a specific elliptic curve, discussing counting points over finite fields as well as constructing an associated $L$-function and pinning down the affiliated special value $L(E, 1)$ for the elliptic curve $E$ primarily discussed throughout this piece. The techniques and tools presented can be carried over to infinitely many elliptic curves partitioned into two sets depending on 'twists' of two specific curves; one of which happens to be the curve previously, and vaguely, mentioned.

Comments: 17 Pages.

Download: PDF

Submission history

[v1] 2017-10-29 21:39:34

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