refs.bib

@book{Silverman:1338326,
      author        = "Silverman, Joseph H",
      title         = "{The Arithmetic of Elliptic Curves}",
      publisher     = "Springer",
      address       = "Dordrecht",
      series        = "Graduate texts in mathematics",
      year          = "2009",
      url           = "https://cds.cern.ch/record/1338326",
      doi           = "10.1007/978-0-387-09494-6",
}

@book{stein2008elementary,
  title={Elementary Number Theory: Primes, Congruences, and Secrets: A Computational Approach},
  author={Stein, W.},
  isbn={9780387855257},
  lccn={2008939895},
  series={Undergraduate Texts in Mathematics},
  url={https://books.google.com/books?id=5hYd0yX4mrMC},
  year={2008},
  publisher={Springer New York}
}

@article{Fitchett,
author = {Fitchett, Stephanie},
year = {2023},
month = {05},
pages = {},
title = {Bezout's Theorem: A taste of algebraic geometry}
}

@article{Kline,
author = {Kline, Daniel},
year = {2023},
month = {05},
pages = {},
title = {Elliptic Curves and Cryptography}
}

@book{cassels_1991, 
place={Cambridge}, 
series={London Mathematical Society Student Texts}, 
title={LMSST: 24 Lectures on Elliptic Curves}, 
DOI={10.1017/CBO9781139172530}, 
publisher={Cambridge University Press}, 
author={Cassels, J. W. S.}, 
year={1991}, 
collection={London Mathematical Society Student Texts}}

@book{nichols2013intersection,
  title={Intersection Number of Plane Curves},
  author={Nichols, M.E.},
  url={https://books.google.com/books?id=UMUbnQAACAAJ},
  year={2013},
  publisher={Oberlin College}
}
@book{sandifer2007euler,
  title={How Euler Did It},
  author={Sandifer, C.E.},
  isbn={9780883855638},
  lccn={2007927658},
  series={MAA spectrum},
  url={https://books.google.com/books?id=sohHs7ExOsYC},
  year={2007},
  publisher={Mathematical Association of America}
}

@book{legendre,
  title={Trait{\'e} des fonctions elliptiques et des int{\'e}grales eul{\'e}riennes: avec des tables pour en faciliter le calcul num{\'e}rique},
  author={Legendre, A.M.},
  number={v. 1},
  lccn={04007777},
  series={Trait{\'e} des fonctions elliptiques et des int{\'e}grales eul{\'e}riennes: avec des tables pour en faciliter le calcul num{\'e}rique},
  url={https://books.google.com/books?id=IC\_vAAAAMAAJ},
  year={1825},
  publisher={Imprimerie de Huzard-Courcier}
}

@book{jacobi1829fundamenta,
  title={Fundamenta nova theoriae functionum ellipticarum},
  author={Jacobi, C.G.J.},
  url={https://books.google.com/books?id=wLKbL6-GwhUC},
  year={1829},
  publisher={Sumtibus fratrum}
}

@article{abel,
author = {M. N. H. Abel},
title = {{Recherches sur les fonctions elliptiques}},
volume = {26},
journal = {Acta Mathematica},
number = {none},
publisher = {Institut Mittag-Leffler},
pages = {3 -- 41},
year = {1902},
doi = {10.1007/BF02415484},
URL = {https://doi.org/10.1007/BF02415484}
}

@book{farkas1991riemann,
  title={Riemann Surfaces},
  author={Farkas, H.M. and Kra, I.},
  isbn={9780387977034},
  lccn={91030662},
  series={Graduate Texts in Mathematics},
  url={https://books.google.com/books?id=bGZDU9HxgpAC},
  year={1991},
  publisher={Springer New York}
}

@article{rice,
 ISSN = {0025570X, 19300980},
 URL = {https://www.jstor.org/stable/10.4169/math.mag.85.3.163},
 abstract = {Summary Elliptic curves are a fascinating area of algebraic geometry with important connections to number theory, topology, and complex analysis. As their current ubiquity in mathematics suggests, elliptic curves have a long and fascinating history stretching back many centuries. This paper presents a survey of key points in their development, via elliptic integrals and functions, closing with an explanation of why no elliptically-shaped planar curved line may ever be called an elliptic curve.},
 author = {Adrian Rice and Ezra Brown},
 journal = {Mathematics Magazine},
 number = {3},
 pages = {pp. 163--176},
 publisher = {[Mathematical Association of America, Taylor & Francis, Ltd.]},
 title = {Why Ellipses Are Not Elliptic Curves},
 urldate = {2023-05-09},
 volume = {85},
 year = {2012}
}

@article{H1901,
author = {H. Poincaré},
journal = {Journal de Mathématiques Pures et Appliquées},
language = {fre},
pages = {161-234},
title = {Sur les propriétés arithmétiques des courbes algébriques},
url = {http://eudml.org/doc/235835},
volume = {7},
year = {1901},
}

@book{singh1998fermat,
  title={Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem},
  author={Singh, S. and Lynch, J.},
  isbn={9780385493628},
  lccn={98027262},
  url={https://books.google.com/books?id=wkJ6QaC90c0C},
  year={1998},
  publisher={Knopf Doubleday Publishing Group}
}

@book{miller1986use,
  title={Use of elliptic curves in cryptography},
  author={Miller, Victor S},
  year={1986},
  publisher={Springer}
}

@article{fujii,
author = {Fujii, Kazuyuki and Oike, Hiroshi},
year = {2017},
month = {01},
pages = {649-659},
title = {An Algebraic Proof of the Associative Law of Elliptic Curves},
volume = {07},
journal = {Advances in Pure Mathematics},
doi = {10.4236/apm.2017.712040}
}