Research Articles

39. Ranks of elliptic curves with j-invariant 1728 (with Erik Wallace), in preparation.

38. Twists of elliptic curves (with Michael Chou), in preparation.

37. Rank growth in quadratic extensions (with Dylan Costa), in preparation.

36. Models of CM elliptic curves with a prescribed ell-adic image (with Enrique González-Jiménez and Benjamin York), in preparation.

35. Elliptic curves with complex multiplication and abelian division fields (with Asimina S. Hamakiotes). (arXiv preprint: 2308.00668.)

34. How to referee a (math) paper, in Notices of the AMS, 71-74 (January 2023).

33. The Day She Proved It, in The Mathematical Intelligencer, 44, 273-276 (2022).

32. Towards a classification of entanglements of Galois representations attached to elliptic curves (with Harris Daniels and Jackson Morrow), in Revista Matematica Iberoamericana, Vol. 39, No. 3, pp. 803-844. (arXiv preprint:2105.02060).

31. Coincidences of division fields (with Harris Daniels), in Annales de l’Institut Fourier, Volume 73 (2023) no. 1, pp. 163-202. (arXiv preprint: 1912.05618.)

30. Galois representations attached to elliptic curves with complex multiplication, in Algebra and Number Theory, 16:4 (2022). (arXiv preprint: 1809.02584.)

29. A classification of isogeny-torsion graphs of elliptic curves over Q (with Garen Chiloyan), in Transactions of the London Mathematical Society, Volume 8, Issue 1, December 2021, 1-34. (arXiv preprint: 2001.05616.) Magma Code.

28. Rank and bias in families of hyperelliptic curves via Nagao’s conjecture (with Trajan Hammonds, Seoyoung Kim, Benjamin Logsdon, and Steven J. Miller), in Journal of Number Theory, Volume 215October 2020, Pages 339-361. (arXiv preprint: 1906.09407.)

27. Bounds of the rank of the Mordell–Weil group of jacobians of hyperelliptic curves (with Harris Daniels, and Erik Wallace), in Journal de Théorie des Nombres de Bordeaux, Vol 32 (2020), no. 1, 231–258. (arXiv preprint: 1708.07896.)

26. A probabilistic model for the distribution of ranks of elliptic curves over Q, in Journal of Number Theory, Volume 221, April 2021, 270-338. (arXiv preprint: 1611.01999.)

25. On the torsion of rational elliptic curves over quartic fields (with Enrique González-Jiménez), in Mathematics of Computation87 (2018), 1457-1478.

24. Uniform boundedness in terms of ramification, in Research in Number Theory, 2018, 4:6.

23. Torsion subgroups of rational elliptic curves over the compositum of all cubic fields (with Harris Daniels, Filip Najman, and Andrew Sutherland), arXiv preprint: 1509.00528 (current version corrects an error in the proofs of Lemma 3.2 and Theorem 3.6), in Mathematics of Computation, 87 (2018), 425-458.

22. On the minimal degree of definition of p-primary torsion subgroups of elliptic curves (with Enrique González-Jiménez), in Mathematical Research Letters., Vol 24 (2017), Num. 4, pp. 1067-1096. Magma scripts.

21. What is… an elliptic curve? (with Harris Daniels), in the Notices of the American Mathematical Society., Vol 64, Issue 3, March 2017, pp. 241-243. (Published version)

20. Premio Abel 2016: Andrew J. Wiles, in La Gaceta de la RSME (J. of the Royal Mathematical Society of Spain), Vol 20 (2017), Num. 1, pp. 57-82.

19. Elliptic curves with abelian division fields (with Enrique González-Jiménez), in Mathematische ZeitschriftAugust 2016, Volume 283, Issue 3, pp. 835–859.

18. Ramification in the division fields of elliptic curves with potential supersingular reduction, in Research in Number Theory 2016 2:8, pp. 1-25.

17. On the number of isomorphism classes of CM elliptic curves defined over a number field (with Harris Daniels), in the Journal of Number Theory, Volume 157, December 2015, pp. 367–396.

16. Division fields of elliptic curves with minimal ramification, in the Revista Matematica Iberoamericana, Volume 31, Issue 4, 2015, pp. 1311–1332.

15. On the field of definition of p-torsion points on elliptic curves over the rationals, in the Mathematische Annalen, Vol 357, Issue 1 (2013), pp. 279-305.

14. Formal Groups of Elliptic Curves with Potential Good Supersingular Reduction, in the Pacific Journal of Mathematics, 261 (2013), n. (1), pp. 145-164.

13. Desde Fermat, Lamé y Kummer hasta Iwasawa: Una introducción a la teoría de IwasawaLa Gaceta de la Real Sociedad Matemática Española (J. of the Royal Mathematical Society of Spain), Volumen 15, numero 2 (2012), pp. 251-276.

12. Bernoulli-Hurwitz numbers, Wieferich primes and Galois representationsJournal of Number Theory, 130 (2010), Issue 3, pp. 539-558.

11. Bounds for the torsion of elliptic curves over extensions with bounded ramification (joint with Benjamin Lundell), in International Journal of Number TheoryVolume: 6, Issue: 6  (2010), pp. 1293-1309.

10. Elliptic curves of maximal rank, (joint work with Julian Aguirre and Juan Carlos Peral), in Revista Matematica Iberoamericana, proceedings of the conference “Segundas Jornadas de Teoria de Numeros”. (2010), pp. 1-28.

9. On the product of twists of rank two and a conjecture of Larsen, in Ramanujan Journal, Vol 19, n 1, May 2009, pp. 53-61.

8. On products of quadratic twists and ranks of elliptic curves over large fields (joint with Bo-Hae Im), in Journal of the London Mathematical Society, Vol 79, part 1, Feb. 2009, pp. 1-14.

7. Ranks of abelian varieties over infinite extensions of the rationals, in Manuscripta Mathematica, Volume 126, Number 3,  July 2008, pp. 393-407.

6. Bernoulli numbers, Hurwitz numbers, p-adic L-functions and Kummer’s criterion, in RACSAM (Journal of the Royal Academy of Science of Spain), Vol 101 (1), 2007, pp. 1-32.

5. Constructing elliptic curves over Q(t) with moderate rank (joint with Scott Arms and Steven J.Miller), in Journal of Number Theory, Volume 123, Issue 2, April 2007, pp. 388-402.

4. On elliptic units and p-adic Galois representations attached to elliptic curves, in Journal of Number Theory, Vol. 117, Issue 2, (2006), pp. 439-470.

3. On the surjectivity of Galois representations attached to elliptic curves over number fields, in Acta Arithmetica, Vol. 117, No. 3, (2005), pp. 283-291.

2. On certain closed subgroups of SL(2,Z_p[[X]]), in Revista Colombiana de Matemáticas, Vol 39 (2005), pp. 13-19.

1. Buscando puntos racionales en curvas elípticas: Métodos explícitos in La Gaceta de la Real Sociedad Matematica Española (J. of the Royal Mathematical Society of Spain), Vol. 8 (2005), n 2, 471-488.


MathSciNet Contributed Reviews


  • Magma code to define one elliptic curve over Q for each of the 13 rational j-invariants with complex multiplication.