An improved lower bound on the greatest element of a sum-distinct set of fixed order. - Noam D. Elkies (J. Comb. Theory A, 1986)

Heegner point computations. - Noam D. Elkies (ANTS, 1994)

Shimura Curve Computations. - Noam D. Elkies (ANTS, 1998)

Rational Points Near Curves and Small Nonzero |x3-y2| via Lattice Reduction. - Noam D. Elkies (ANTS, 2000)

Excellent codes from modular curves. - Noam D. Elkies (STOC, 2001)

Mordell-Weil Lattices in Characteristic 2, III: A Mordell-Weil Lattice of Rank 128. - Noam D. Elkies (Exp. Math., 2001)

Endgame Tables and Chess Composition. - Noam D. Elkies (J. Int. Comput. Games Assoc., 2001)

Trinomials ax and ax with Galois Groups of Order 168 and 8·168. - Nils Bruin; Noam D. Elkies (ANTS, 2002)

Curves Dy=x-x of Odd Analytic Rank. - Noam D. Elkies (ANTS, 2002)

New Optimal Tame Towers of Function Fields over Small Finite Fields. - Wen-Ching W. Li; Hiren Maharaj; Henning Stichtenoth; Noam D. Elkies (ANTS, 2002)

On the Sums. - Noam D. Elkies (Am. Math. Mon., 2003)

Elliptic Curves x3 + y3 = k of High Rank. - Noam D. Elkies; Nicholas F. Rogers (ANTS, 2004)

Elliptic Curves of Large Rank and Small Conductor. - Noam D. Elkies; Mark Watkins (ANTS, 2004)

New Directions in Enumerative Chess Problems. - Noam D. Elkies (Electron. J. Comb., 2005)

Points of Low Height on Elliptic Curves and Surfaces I: Elliptic Surfaces over mathbb P1 with Small d. - Noam D. Elkies (ANTS, 2006)

Shimura Curves for Level-3 Subgroups of the (2, 3, 7) Triangle Group, and Some Other Examples. - Noam D. Elkies (ANTS, 2006)

Sylvester-Gallai Theorems for Complex Numbers and Quaternions. - Noam D. Elkies; Lourens M. Pretorius; Conrad Johann Swanepoel (Discret. Comput. Geom., 2006)

The Mathieu Group M 12 and Its Pseudogroup Extension M 13. - John H. Conway; Noam D. Elkies; Jeremy L. Martin (Exp. Math., 2006)

On some points-and-lines problems and configurations. - Noam D. Elkies (Period. Math. Hung., 2006)

The D 4 Root System Is Not Universally Optimal. - Henry Cohn; John H. Conway; Noam D. Elkies; Abhinav Kumar (Exp. Math., 2007)

Shimura Curve Computations Via K3 Surfaces of Néron-Severi Rank at Least 19. - Noam D. Elkies (ANTS, 2008)

Curves of genus 2 with many rational points via K3 surfaces (abstract only). - Noam D. Elkies (ACM Commun. Comput. Algebra, 2008)

On the Classification of Type II Codes of Length 24. - Noam D. Elkies; Scott Duke Kominers (SIAM J. Discret. Math., 2010)

Permutations that Destroy Arithmetic Progressions in Elementary p-Groups. - Noam D. Elkies; Ashvin A. Swaminathan (Electron. J. Comb., 2017)

Fast evaluation of Riemann theta functions in any dimension. - Noam D. Elkies; Jean Kieffer (CoRR, 2025)