Research

Papers

Tables

Software

Research:

Number Theory: Elliptic curves, Hyperelliptic curves, Modular curves, Modular Abelian Varieties, Arithmetic progression, Diophantine equations.

MathSciNet	ZbMath	Orcid	ResearchID	Scopus	GoogleScholar	arXiv
703386		0000-0002-0469-5431	G-9383-2015	8380999800

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Papers:

37. Squares in arithmetic progression over certain non-primitive quartic number fields (joint with Nguyen Xuan Tho). Submitted
38. Quadratic points on the Fermat quartic over number fields. Submitted
39. Parametrization of isogeny-torsion graphs of elliptic curves defined over Q .
    
40. Faltings ellipitc curves in twisted Q-isogeny classes, (joint with J.C. Lario). arxiv data Submitted .


41. Models of CM elliptic curves with a prescribed l-adic Galois image, (joint with Álvaro Lozano-Robledo and Benjamin York). Journal of Number Theory 277 (2025) 19-62. doi data
42. Torsion growth over cubic fields of rational elliptic curves with complex multiplication, Publicationes Mathematicae Debrecen 97/1-2, 63-76 (2020). pdf doi data
43. Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields, Glasnik Matematički 56(76)(2021), 47-61. pdf doi data
44. An algorithm for determining torsion growth of elliptic curves (joint with F. Najman). Experimental Mathematics 32 (2023) 70-81 doi data
    
45. Serre's constant of elliptic curves over the rationals (joint with H.B. Daniels). Experimental Mathematics 31 (2022) 518-532 pdf doi data
    
46. On the torsion of rational elliptic curves over sextic fields (joint with H.B. Daniels). Mathematics of Computation 89 (2020) 411-439. pdf doi data
47. Growth of torsion groups of elliptic curves upon base changes (joint with F. Najman). Mathematics of Computation 89 (2020) 1457-1485 pdf errata doi data
48. Complete classification of the torsion structures of rational elliptic curves over quintic number fields. Journal of Algebra 478 (2017) 484–505. pdf doi data
49. On the torsion of rational elliptic curves over quartic fields (joint with Á. Lozano-Robledo). Mathematics of Computation 87 (2018) 1457-1478. pdf doi data
50. On the minimal degree of definition of p-primary torsion subgroups of elliptic curves (joint with Á. Lozano-Robledo). Mathematical Research Letter 24 (2017) 1067-1096. pdf doi data
    
51. Elliptic Curves with abelian division fields (joint with Á. Lozano-Robledo). Mathematische Zeitschrift 283, 835-859 (2016). pdf doi data
52. Torsion of rational elliptic curves over cubic fields (joint with F. Najman and J.M. Tornero). Rocky Mountain Journal of Mathematics 46 (2016) 1899-1917. pdf doi
    
53. Torsion of rational elliptic curves over quadratic fields II (joint with J.M. Tornero). Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemática, 110 (1) (2016), 121-143. pdf. doi
    
54. Covering techniques and rational points on some genus 5 curves. Contemporary Mathematics AMS (2015) 649, 89-105 pdf doi
    
55. On arithmetic progressions on Edwards curves. Acta Arithmetica 167 (2015), 117-132. pdf doi
    
56. Torsion of rational elliptic curves over quadratic fields (joint with J.M. Tornero). Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 108 (2) (2014), 923-934. pdf doi
    
57. On a conjecture of Rudin on squares in arithmetic progressions (joint with X. Xarles). LMS Journal of Computation and Mathematics 17 (1) (2014), 58-76. pdf doi data
    
58. Markoff-Rosenberger triples in geometric progression. Acta Mathematica Hungarica 142 (1) (2014), 231-243. pdf doi
    
59. Five squares in arithmetic progression over quadratic fields (joint with X. Xarles). Revista Matemática Iberoamericana 29, no. 4, 1211-1238 (2013). pdf doi data
60. Markoff-Rosenberger triples in arithmetic progression (joint with J.M. Tornero). Journal of Symbolic Computation 53, 53-63 (2013). pdf doi data
61. On symmetric square values of quadratic polynomials (joint with X. Xarles). Acta Arithmetica 149, 145-159 (2011). pdf doi data.
62. On fields of definition of torsion points of elliptic curves with complex multiplication (joint with L. Dieulefait and J. Jiménez Urroz). Proceedings of the American Mathematical Society 139, no. 6, 1961-1969 (2011). pdf data doi
63. Three cubes in arithmetic progression over quadratic fields. Archiv der Mathematik Vol. 95, no. 3, 233-241 (2010). pdf doi
64. On the ubiquity of trivial torsion on elliptic curves (joint with J.M. Tornero). Archiv der Mathematik Vol. 95, no. 2, 135-141 (2010). pdf doi
65. Arithmetic progressions of four squares over quadratic fields (joint with J. Steuding). Publicationes Mathematicae Debrecen 77, 1-2, 125-138 (2010). pdf doi
66. On the modularity level of modular abelian varieties over number fields (joint with X. Guitart). Journal of Number Theory 130, no. 7, 1560-1570 (2010). pdf doi
67. Galois theory, discriminants and torsion subgroup of elliptic curves (joint with I. García-Selfa and J.M. Tornero). Journal of Pure and Applied Algebra 214, 1340-1346 (2010). pdf doi
68. Non-hyperelliptic modular curves of genus 3 (joint with R. Oyono). Journal of Number Theory 130, no. 4, 862-878 (2010). pdf doi
    
69. Right triangles with algebraic sides and elliptic curves over number fields (joint with E. Girondo, G. González-Diez, R. Steuding and J. Steuding). Mathematica Slovaca 59, no. 3, 299-306 (2009). pdf doi
70. Finiteness Results for modular curves of genus at least 2 (joint with M. Baker, J. González and B. Poonen). American Journal of Mathematics 127, no. 6, 1325-1387, (2005). pdf doi
71. On the Brauer class of modular endomorphism algebras (joint with E. Ghate and J. Quer). International Mathematics Research Notices 2005 no. 12, 701-723, (2005). pdf doi
72. Modular curves of genus 2 (joint with J. González). Mathematics of Computation 72, no. 241, 397—418, (2003). pdf doi data
73. Computations on Modular jacobians surfaces (joint with J. González and J. Guàrdia). Algorithmic number theory (Sydney, 2002), 189-197, LNCS 2369, Springer, Berlin, (2002). pdf doi
74. Curves of genus 2 parametrized from modular curves (joint with J. González). Actas EACA VII, 177-185 (2001).
    
    

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Books:

• Proceedings of the Segundas Jornadas de Teoría de Números (joint with J. Cilleruelo, A. Quirós, X. Xarles (eds.)). Biblioteca de la Revista Iberoamericana de Matemáticas vol. 4 (2008). ISBN 978-84-612-8007-0.
• Curvas Hiperelípticas Modulares. Ph.D.thesis (in Spanish), January 2002. Abstract: English, Spanish
• Curvas elípticas: Grupo de puntos racionales y curvas de rango alto. Master thesis (in Spanish), January 1998. pdf

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Software:

• Modular Curves of Given Level and Genus. On Magma ≥ v2.18.
• Modular Curves of Given Level and Genus (Documentation) (joint with Michael Harrison). Handbook of Magma functions ≥ v.2.18-3 (2012). online

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Tables:

• Torsion Growth of rational elliptic curves over number fields: Table11 and LMFDB
• New Modular Hyperelliptic Curves
• New modular non-hyperelliptic curves of genus 3
• Genus 2 curves with modular jacobians
• Modular Q-curves

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Conference Organizer:

• SAGE Days 16, Barcelona, 22-27 June 2009
• 40 años de Algebra en las Autónomas, Madrid, 21-22 November 2008
• Segundas Jornadas de Teoría de Números, Madrid, 16-19 July 2007
• International Conference on Arithmetic Algebraic Geometry, El Escorial (Madrid), 4-8 September 2006
• Décimas Jornadas de Teoría de Números, Madrid, 8-12 July 2024

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