Andrew V. Sutherland Genus 1:
Genus 2:
Genus 3:
drew@math.mit.edu
I am a Research Scientist here in the math department at MIT, focusing on computational number theory.
Here is a fairly recent photograph.
Announcements
Home page for 18.783, a new course on elliptic curves, to be offered spring 2012.
Sato-Tate distributions in genus 1, 3 total, 2 over Q (updated October 2011).
Sato-Tate distributions in genus 2, 52 total, 34 over Q (updated October 2011).
Defining equations for X1(N) for N up to 190 (December 2010).
Elliptic curve point-counting record over a 5011-digit prime field using the new quadratic-space algorithm (July 2010).
Elliptic curve constructed using the CM method with |D| > 1016 (May 2010).
Publications
Accelerating the CM method, to appear in the London Mathematical Society Journal of Computation and Mathematics.
On the evaluation of modular polynomials, Algorithmic Number Theory 10th International Symposium (ANTS X), 2012.
Deterministic elliptic curve primality proving for a special sequence of numbers, with Alexander Abatzoglou, Alice Silverberg, and Angela Wong, 2Algorithmic Number Theory 10th International Symposium (ANTS X), 2012.
Sato-Tate distributions and Galois endomorphism modules in genus 2, with Francesc Fité, Kiran Kedlaya, and Victor Rotger, to appear in Compositio Mathematica.
The probability that the number of points on the Jacobian of a genus 2 curve is prime, with Wouter Castryck, Amanda Folsom, and Hendrik Hubrechts, to appear in Proceedings of the London Mathematical Society.
A local-global principle for rational isogenies of prime degree, to appear in Journal de Théorie des Nombres de Bordeaux.
A low-memory algorithm for finding short product representations in finite groups, with Gaetan Bisson, Designs, Codes, and Cryptography 63 (2012), pp. 1-13.
Constructing elliptic curves with prescribed torsion over finite fields, Mathematics of Computation 81 (2012), pp. 1131-1147.
Modular polynomials via isogeny volcanoes, with Reinier Bröker and Kristin Lauter, Mathematics of Computation 81 (2012), pp. 1201-1231.
Computing Hilbert class polynomials with the Chinese Remainder Theorem, Mathematics of Computation 80 (2011), pp. 501-538.
Structure computation and discrete logarithms in finite abelian p-groups, Mathematics of Computation 80 (2011), pp. 477-500.
Computing the endomorphism ring of an ordinary elliptic curve over a finite field, with Gaetan Bisson, Journal of Number Theory, 113 (2011), pp. 815-831.
Class invariants by the CRT method, with Andreas Enge, Algorithmic Number Theory 9th International Symposium (ANTS IX), LNCS 6197, Springer, 2010, pp. 142-156.
An explicit height bound for the classical modular polynomial, with Reinier Bröker, Ramanujan Journal 22 (2010), pp. 293-313.
On a theorem of Mestre and Schoof, with John E. Cremona, Journal de Théorie des Nombres de Bordeaux 22 (2010), pp. 353-358.
Hyperelliptic curves, L-polynomials, and random matrices,
with Kiran S. Kedlaya, Arithmetic, Geometry, Cryptography and Coding Theory (AGCT-11, 2007), Contemporary Mathematics 487, AMS, 2009, pp. 119-162.
A generic approach to searching for Jacobians, Mathematics of Computation 78 (2009), pp. 485-507.
Computing L-series of hyperelliptic curves,
with Kiran S. Kedlaya, Algorithmic Number Theory 8th International Symposium (ANTS VIII), LNCS 5011, Springer, 2008, pp. 312-326.
Order computations in generic groups, PhD thesis, Massachusetts Institute of Technology, 2007 (Errata).
Winner of the George M. Sprowls Award for Outstanding Thesis in Computer Science.
Preprints
Sato-Tate distributions of twists of y2=x5-x and y2=x6+1, with Francesc Fité, 2012.
On the distribution of Atkin and Elkies primes, with Igor E. Shparlinski, 2011.
Identifying supersingular elliptic curves, 2011.
Talks
Identifying supersingular elliptic curves, 2012 Joint Mathematics Meetings, January 2012
Sato-Tate distributions in genus 2, Boston University, November 2011
Telescopes for mathematicians, Computational Research in Boston and Beyond (MIT), September 2011
Hyperelliptic curves, L-polynomials, and random matrices, MSRI and Emory, February 2011
Genus 1 point counting in quadratic space and essentially quartic time, Columbia-CUNY-NYU, September 2010
Class invariants by the CRT method, ANTS IX, July 2010
A local-global principle for rational isogenies of prime degree, CNTA XI, July 2010
L-polynomial distributions of genus 2 curves, ETH Zurich, May 2010
Genus 1 point counting in quadratic space and essentially quartic time, CRM Montreal, April 2010
Decomposing class polynomials with the CRT method, CRM Montreal, April 2010
Modular polynomials via isogeny volcanoes, CCR Princeton, February 2010
Computing the image of Galois representations attached to an elliptic curve, Clay Mathematics Institute, December 2009
Computing modular polynomials with the Chinese Remainder Theorem, ECC 2009 August 2009
Powered by volcanoes: Three new algorithms, Fields Institute, May 2009
Computing the endomorphism ring of an ordinary elliptic curve, CCR La Jolla, April 2009
Sato-Tate in genus 2, MIT, March 2009
Computing class polynomials with the Chinese Remainder Theorem, Microsoft Research, November 2008
Computing Hilbert class polynomials with the CRT method, ECC 2008, September 2008
Computing L-series of hyperelliptic curves, ANTS VIII, May 2008
Subexponential performance from generic group algorithms, MIT, April 2008
Thesis defense, MIT, spring 2007
Beating the birthday paradox, MIT, spring 2007
Data
Table of factored norms of singular moduli
Record CM constructions of elliptic curves
Modular polynomials for the Weber ƒ function
Pairing-friendly Edwards curves of near-prime order with embedding degree 6
Pairing-friendly curves of prime order with embedding degree 6
Pairing-friendly curves of prime order with embedding degree 10
Defining equations for X1(N) in raw form for N ≤ 101
Alternative defining equations for X1(N) for N ≤ 190
Optimized equations for X1(N) for N ≤ 50
Sato-Tate distributions in genus 1.
Sato-Tate distributions in genus 2.
Standard L-polynomial coefficient distributions in genus 1, 2, and 3
101 useful trace zero varieties
Gallery of large Jacobians
Software
smoothrelation_v11.tar, as described in Computing the endomorphism ring of an ordinary elliptic curve over a finite field. (Version 1.1 includes an important bug fix)
smalljac_v3.tar, as described in Computing L-series of hyperelliptic curves, with some futher optimizations (Version 4.0 to be posted soon).
galrep_v0.tar, as described in Computing the image of Galois representations attached to an elliptic curve, preliminary version.
galrep_ecdata_big.dat, auxiliary elliptic curve data for more extensive galrep computations (approx 104 MB)
galrep_gl2data_big.dat, auxiliary GL(2,Z/ellZ) conjugacy class data for more extensive galrep computations (approx 4 MB)
Genus 3:
