Are covered in david kohel's phd thesis  and more recently in [8, 9] 13 complexity model unless otherwise stated all complexity estimations in this paper use elementary bit- wise operations as units we use the standard “big o notation” to describe asymptotic complexities of algorithms recall that for any two functions. Such graphs the definitive work in this area was done by david kohel, whose thesis explicates the structure of isogeny graphs of elliptic curves over finite fields  the term “volcano” came later, in work by fouquet and morain [14, 15] that popularized kohel's work and gave one of the first examples of. Thesis  1 introduction let a be an absolutely simple abelian variety of dimension g defined over a field with q elements its frobenius endomorphism π 118–138 doi: 101112/s1461157000000097  david r kohel “ endomorphism rings of elliptic curves over finite fields” phd thesis university of california at. Endomorphism rings of elliptic curves over nite elds by david kohel bs biochemstry (texas a&m university) 1989 bs mathematics (texas a&m university) 1989 candidate in philosophy (university of california, berkeley) 1992 a dissertation submitted in partial satisfaction of the requirements for the degree of. Prof dr bas edixhoven prof dr david r kohel (université de la méditerranée) prof dr hendrik w lenstra jr the main theme of this thesis is making these constructions explicit for the case where the we define notions that occur in every chapter of this thesis, and we state the 'main theorem' of the theory of complex. Une région explicite sans zéro pour les fonctions l de dirichlet, phd thesis, habiba kadiri, université des sciences et technologie de lille 2001 arithmetic, geometry, cryptography and coding theory 2009, edited by: david kohel and robert rolland, contemporary mathematics 521, september 2010.
David jao, stephen d miller, ramarathnam venkatesanexpander graphs based on grh with an application to elliptic curve cryptography j number theory, 129 (6) (2009), pp 1491-1504 : david kohel, endomorphism rings of elliptic curves over finite fields, phd thesis of the university of california at berkeley, 1996. A thesis submitted in fulfilment of the requirements for the degree of statement this thesis contains no material which has been accepted for the award of david kohel his patience, insight, and leadership have been a constant source of inspiration to me it has been a privelege to learn mathematics with him thanks to. 5011, springer, 2008, pp 312-326 mr 2467855 46 david kohel, endomorphism rings of elliptic curves over finite fields, phd thesis, university of california at berkeley, 1996 47 daniel sion kubert, universal bounds on the torsion of elliptic curves, proceedings of the london mathematical society 33 ( 1976), 193-237.
Details about computations with supersingular curves see kohel  and mestre  the paper is organised as methods of kohel's thesis  to construct an isogenous elliptic curve e /fp such that end(e ) = z[π] for instance, as david kohel has pointed out, an isogeny is defined as a map of one dimensional group. John voight, associate professor of mathematics, dartmouth college. Thesis: several new proofs for maximum modulus principle of functions of several complex variables advisor: prof min wu outstanding master's thesis award 2010, tsinghua university (unique awardee of de- partment of mathematical sciences) (with david kohel and igor shparlinski) publications 1 counting.
In his seminal thesis, kohel describes the structure of the graph of isogenies defined on ellt ( q ) 2 preliminaries kohel's algorithm treats each large prime power pk dividing v by computing the kernel of a david kohel, endomorphism rings of elliptic curves over finite fields, phd thesis of the university of california at. Thanks a lot for the references, they should be very helpful i was also pointed to david kohel's thesis, where (among other results) he provides bounds on the number of elliptic curves isogenous to a given curve c via an isogeny of a given degree he also uses brandt matrices – vesna stojanoska jan 23.
David had implemented code for computing with quaternion algebras, and this was the only implementation of that algorithm in the world my algorithm fundamentally relied on exactly the computations in rational quaternion algebras that david kohel had implemented in magma i had a thesis to finish. The first paper about this topic was my paper constructing isogenies between elliptic curves over finite fields (relying heavily on david kohel's phd thesis) a more useful formulation of the result was given by jao, miller and venkatesan in the paper “do all elliptic curves of the same order have the same.