29 citations · 35 across the 4 of their papers we have counts for
4 papers
The Mathieu group and its pseudogroup extension
John H. Conway, Noam D. Elkies, Jeremy L. Martin
We study a construction of the Mathieu group using a game reminiscent of Loyd's ``15-puzzle''. The elements of are realized as permutations on~12 of the~13 points…
Elliptic Curves x^3 + y^3 = k of High Rank
Noam D. Elkies, Nicholas F. Rogers
We use rational parametrizations of certain cubic surfaces and an explicit formula for descent via 3-isogeny to construct the first examples of elliptic curves E_k: x^3 + y^3 = k o…
Elliptic curves of large rank and small conductor
Noam D. Elkies, Mark Watkins
For r=6,7,...,11 we find an elliptic curve E/Q of rank at least r and the smallest conductor known, improving on the previous records by factors ranging from 1.0136 (for r=6) to ov…
Sylvester-Gallai Theorems for Complex Numbers and Quaternions
Noam Elkies, Lou M. Pretorius, Konrad J. Swanepoel
A Sylvester-Gallai (SG) configuration is a finite set S of points such that the line through any two points in S contains a third point of S. According to the Sylvester-Gallai Theo…