# Elliptic Curves as Algebraic Structures

DevFeed: [Elliptic Curves as Algebraic Structures](<https://devfeed.tech/articles/elliptic-curves-as-algebraic-structures-40345.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2014/02/16/elliptic-curves-as-algebraic-structures/>)

Published: 2014-02-16T10:00:39Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [structure](<https://devfeed.tech/topics/structure.md>), [Cryptography](<https://devfeed.tech/topics/cryptography.md>)

Tags: [algorithm](<https://devfeed.tech/tags/algorithm.md>), [cryptography](<https://devfeed.tech/tags/cryptography.md>), [elliptic-curves](<https://devfeed.tech/tags/elliptic-curves.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [points](<https://devfeed.tech/tags/points.md>), [structure](<https://devfeed.tech/tags/structure.md>)

## AI overview

This mathematical tutorial explains elliptic curves as algebraic structures. It develops the geometric algorithm for adding points by drawing a line through two points, finding the third intersection with the curve, and reflecting that point across the x-axis.

## Source excerpt

Last time we looked at the elementary formulation of an elliptic curve as the solutions to the equation $$y^2 = x^3 + ax + b$$ where $ a,b$ are such that the discriminant is nonzero: $$-16(4a^3 + 27b^2) \neq 0$$ We have yet to explain why we want our equation in this form, and we will get to that, but first we want to take our idea of intersecting lines as far as possible.