Journal Article

Bharagava , Manjul , Cremona, J. E. and Fisher, Tom (2020) The proportion of genus one curves over Q defined by a binary quartic that everywhere locally have a point. International Journal of Number Theory . doi:10.1142/S1793042121500147 (In Press)

Cremona, J. E. and Pacetti, Ariel (2019) On elliptic curves of prime power conductor over imaginary quadratic fields with class number one. Proceedings of the London Mathematical Society, 118 (5). pp. 1245-1276. doi:10.1112/plms.12214

Argaez-Garcia, Alejandro and Cremona, J. E. (2018) Black box Galois representations. Journal of Algebra, 512 . pp. 526-565. doi:10.1016/j.jalgebra.2018.05.017

Bhargava, Manjul, Cremona, J. E. and Fisher, Tom (2016) The proportion of plane cubic curves over Q that everywhere locally have a point. International Journal of Number Theory, 12 (4). 1077. doi:10.1142/S1793042116500664

Cremona, J. E. (2016) The L-functions and modular forms database project. Foundations of Computational Mathematics . doi:10.1007/s10208-016-9306-z

Bhargava, Manjul, Cremona, J. E., Fisher, Tom, Jones, Nick G. and Keating, Jonathan P. (2016) What is the probability that a random integral quadratic form in n variables has an integral zero? International Mathematics Research Notices, 2016 (12). pp. 3828-3848. doi:10.1093/imrn/rnv251

Bhargava, Manjul, Cremona, J. E., Fisher, Tom, Jones, Nick G. and Keating, Jonathan P. (2015) What is the probability that a random integral quadratic form in n variables has an integral zero? International Mathematics Research Notices . rnv251. doi:10.1093/imrn/rnv251

Cremona, J. E., Fisher, T. A., O'Neil, C., Simon, D. and Stoll, Michael (2014) Explicit n-descent on elliptic curves III. Algorithms. Mathematics of Computation, 84 (292). pp. 895-922. doi:10.1090/S0025-5718-2014-02858-5

Cremona, J. E. and Thongjunthug, Thotsaphon (2013) The complex AGM, periods of elliptic curves over and complex elliptic logarithms. Journal of Number Theory, Volume 133 (Number 8). pp. 2813-2841. doi:10.1016/j.jnt.2013.02.002

Cremona, J. E. and Edjvet, M. (2010) Cyclically presented groups and resultants. International Journal of Algebra and Computation, Vol.20 (No.3). pp. 417-435. doi:10.1142/S0218196710005777

Cremona, J. E., Fisher, Tom A. and Stoll, Michael (2010) Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves. Algebra & Number Theory, Vol.4 (No.6). pp. 763-820. doi:10.2140/ant.2010.4.763

Cremona, J. E. and Sutherland, Andrew V. (2010) On a theorem of Mestre and Schoof. Journal de Théorie des Nombres de Bordeaux, Vol.22 (No.2). pp. 353-358. doi:10.5802/jtnb.719

Cremona, J. E., Fisher, T. A., O'Neil, C., Simon, D. and Stoll, M. (2009) Explicit n-descent on elliptic curves, II. Geometry. Journal fur die reine und angewandte Mathematik, Volume 2009 (Number 632). pp. 63-84. doi:10.1515/CRELLE.2009.050

Cremona, J. E. and Fisher, T. A. (2009) On the equivalence of binary quartics. Journal of Symbolic Computation, Vol.44 (No.6). pp. 673-682. doi:10.1016/j.jsc.2008.09.004

Cremona, J. E., Fisher, T. A., O'Neil, C., Simon, D. (Denis) and Stoll, M. (Michael) (2008) Explicit n-descent on elliptic curves, I. algebra. Journal fur die reine und angewandte Mathematik, Vol.615 . pp. 121-155. doi:10.1515/CRELLE.2008.012

Cremona, J. E. (2008) Unimodular integer circulants. Mathematics of Computation, Vol.77 (No.263). pp. 1639-1652. doi:10.1090/S0025-5718-08-02089-9

Cremona, J. E. and Lingham, M. P. (2007) Finding all elliptic curves with good reduction outside a given set of primes. Experimental Mathematics, Volume 16 (Number 3). pp. 303-312.

Book Item

Best, A. J., Bober, J., Booker, A. R., Costa, E., Cremona, J. E., Derickx, M., Lowry-Duda, D., Lee, M., Roe, D., Sutherland, A. V. and Voight, J. (2021) Computing classical modular forms. In: Hassett, B., (ed.) Arithmetic Geometry, Number Theory, and Computation. Simons Symposia . Springer. (In Press)

Cremona, J. E., Dembele, Lassina, Pacetti, Ariel, Schembri, Ciaran and Voight, John (2021) On rational Bianchi newforms and abelian surfaces with quaternionic multiplication. In: Arithmetic Geometry, Number Theory, and Computation. Simons Symposia . Springer.

Conference Item

Cremona, J. E. (2012) Computational number theory. In: School and Workshop on Computational Algebra and Number Theory, Trieste, Italy, 18-29 Jun 2012 (Unpublished)

Cremona, J. E. (2012) Elusive isogenies and unusual modular curves. In: Atkin Memorial Lecture and Workshop Elliptic Curves over Q(sqrt{5}), Chicago, 27-29 Apr 2012 (Unpublished)

Cremona, J. E. (2011) Sage as a research tool. In: Sage Days (Algorithms in Number Theory and FLINT), University of Warwick, Coventry, 17-22 Dec 2011 (Unpublished)

Cremona, J. E. (2011) Modular symbols over number fields. In: Summer School and Conference : Computations with Modular Forms 2011, University Heidelberg, 5-8 Sep 2011 (Unpublished)

Cremona, J. E. (2011) Number theory software development : a personal and historical view. In: Sage Days 29, Seattle, Washington, 21-25 Mar 2011 (Unpublished)

Cremona, J. E. (2011) Computing elliptic curves using modular symbols. In: Introductory Workshop : Arithmetic Statistics, Berkeley, California, 31 Jan-04 Feb 2011 (Unpublished)

Cremona, J. E. (2011) Numerical evidence for the Birch Swinnerton-Dyer Conjecture. In: Conference on the Birch and Swinnerton-Dyer conjecture, Cambridge, 4-6 May 2011 (Unpublished)

Cremona, J. E. (2010) The complex AGM and periods of elliptic curves over C. In: Sage Days 23 : Number Theory and Computer Algebra, Leiden, The Netherlands, 5-9 Jul 2010 (Unpublished)

Cremona, J. E. (2010) Computing isogenies. In: Sage Days 22 : Computing with Elliptic Curves, Berkeley, California, 21 Jun-02 Jul 2010 (Unpublished)

Cremona, J. E. (2010) Finding all elliptic curves with good reduction outside a given set of primes. In: Sage Days 22 : Computing with Elliptic Curves, Berkeley, California, 21 Jun-02 Jul 2010 (Unpublished)

Cremona, J. E. (2010) Verifying optimality and Manin's conjecture. In: Sage Days 22 : Computing with Elliptic Curves, Berkeley, California, 21 Jun-02 Jul 2010 (Unpublished)

Cremona, J. E. (2010) Tables of elliptic curves. In: Sage Days 22 : Computing with Elliptic Curves, Berkeley, California, 21 Jun-02 Jul 2010 (Unpublished)

Cremona, J. E. (2010) Sage : free, open-source mathematical software that supports research and teaching. In: Bristol Algorithms Days 2010 : Feasibility Workshop, University of Bristol, 15-16 Feb 2010 (Unpublished)

Cremona, J. E. (2009) The complex AGM and periods of elliptic curves over C. In: Théorie des nombres et applications., Marseille, France, 30 Nov-4 Dec 2009 (Unpublished)

Cremona, J. E. (2008) Elliptic curves in Sage. In: Sage days 10, Nancy, France, 10-15 Oct 2008 (Unpublished)

Cremona, J. E. (2008) Computing modular forms over imaginary quadratic fields. In: Workshop: Computations with Modular Forms, University of Bristol, 18-22 Aug 2008 (Unpublished)

Cremona, J. E. (2008) Reduction of binary forms over imaginary quadratic fields. In: 60th British Mathematical Colloquium. University of York, 25-28 Mar 2008., University of York, 25-28 Mar 2008 (Unpublished)

Cremona, J. E. (2008) Computing in component groups of elliptic curves. In: 8th International Symposium on Algorithmic Number Theory, Banff, Canada, May 17-22, 2008. Published in: Algorithmic number theory : 8th international symposium, ANTS-VIII, Banff, Canada, May 17-22, 2008 : proceedings (Lecture Notes in Computer Science), Vol.5011 pp. 118-124. ISBN 978-3-540-79455-4. ISSN 0302-9743. doi:10.1007/978-3-540-79456-1_7

Working or Discussion Paper

Cremona, J. E., Fisher, Tom, O'Neil, Cathy, Simon, Denis and Stoll, Michael (2011) Explicit n-descent on elliptic curves. III. Algorithms. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1107.3516v1).

Cremona, J. E. and Thongjunthug, Thotsaphon (2010) The complex AGM, periods of elliptic curves over C and complex elliptic logarithms. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1011.0914v1).

Journal Item

Carlson, Jon, Cremona, J. E. and O'Brien, Eamonn (2009) Special issue celebrating significant birthdays of John Cannon and Derek Holt. Journal of Algebra, Vol.322 (No.3 Sp. Iss. SI). p. 601. doi:10.1016/j.jalgebra.2009.05.001