---
product_id: 11468835
title: "Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics)"
brand: "joseph h. silvermanjohn tate"
price: "$112.60"
currency: USD
in_stock: true
reviews_count: 10
url: https://www.desertcart.us/products/11468835-rational-points-on-elliptic-curves-undergraduate-texts-in-mathematics
store_origin: US
region: United States of America
---

# Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics)

**Brand:** joseph h. silvermanjohn tate
**Price:** $112.60
**Availability:** ✅ In Stock

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- **What is this?** Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics) by joseph h. silvermanjohn tate
- **How much does it cost?** $112.60 with free shipping
- **Is it available?** Yes, in stock and ready to ship
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## Description

Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics)

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## Customer Reviews

### ⭐⭐⭐⭐⭐ 







  
  
    Good introduction to elliptic curves suitable for undergraduates
  

*by N***A on Reviewed in the United States 🇺🇸 on May 17, 2010*

Elliptic curves have come to occupy a central place in number theory, as the spectacular proof of Fermat's Last Theorem fifteen years ago showed.  They have also found applications to more practical subjects, such as cryptography, so it's fair to say that national security and modern finance depend, at least in part, on what was at one point very abstract, theoretical mathematics.  These are just a few reasons why an undergraduate studying mathematics might care to learn about elliptic curves.The most modern treatments of ECs require a relatively sophisticated background.  One not only needs to know basic algebra, topology, and complex analysis, but also commutative algebra, algebraic number theory, and a bit of algebraic geometry.  The great advantage of this book is that it pares down the required background to almost the bare minimum.  Readers are expected to know the content of an introductory algebra course (groups, rings, and fields for the final chapter), and some elementary number theory, but not much more.  Certainly algebraic geometry is not required, and whatever projective geometry is needed is provided in a helpful appendix.  There are also many exercises in the book, most of which are of an appropriate difficulty.  A small percentage of the problems require substantial dedication and ingenuity to solve, and will serve to challenge most readers.The principal drawback of the accessibility is that theorems are not proven in quite as much generality as one might like.  For example, the Mordell-Weil theorem (the group of rational points on an EC is finitely generated), is really only proven for the special class of curves with a rational point of order 2, and Siegel's theorem on finiteness of integer points is only proven for a special class of cubic curves.  Nevertheless, even these special cases have deep, serious proofs, and the more general proofs use the ideas behind the proofs in this book in a substantial way.  The more accessible presentation of the material in this book will serve many as a good first step towards learning the general proofs of these theorems, should readers decide to continue learning more.The only substantial gripe I have with this book are the errors in it.  Most of these are minor, but some are quite substantial.  Fortunately, Silverman maintains an errata at his website, which actually contains not just corrections but also features he may include in the next edition of this book, should he and Tate ever decide to update it.  Overall, this book is a great place for undergraduates to start learning about a deep and important part of number theory, without needing lots of prerequisites.  The book is also suitable for self-study, as it is well-written, not particularly long, and has lots of useful exercises.

### ⭐⭐⭐⭐⭐ 







  
  
    Excellent
  

*by A***R on Reviewed in the United States 🇺🇸 on April 19, 2017*

This is an excellent introductory text which is very informal in its exposition but gets across the big ideas too. Highly recommend to a bright undergraduate or even a first year graduate student for an introduction to elliptic curves

### ⭐⭐⭐ 







  
  
    The Kindle edition is poorly formatted
  

*by W***A on Reviewed in the United States 🇺🇸 on May 11, 2014*

There are a ton of issues with math not rendering correctly in the Kindle edition, which is distracting and annoying.

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*Last updated: 2026-03-17*