53 citations · 136 across the 14 of their papers we have counts for
17 papers
Generalized class polynomials
Marc Houben, Marco Streng
The Hilbert class polynomial has as roots the j-invariants of elliptic curves whose endomorphism ring is a given imaginary quadratic order. It can be used to compute elliptic curve…
Primitive divisors of elliptic divisibility sequences over function fields with constant j-invariant
Bartosz Naskręcki, Marco Streng
We prove an optimal Zsigmondy bound for elliptic divisibility sequences over function fields in case the -invariant of the elliptic curve is constant. In more detail, given an e…
Primes dividing invariants of CM Picard curves
Pınar Kılıçer, Elisa Lorenzo García, Marco Streng
We give a bound on the primes dividing the denominators of invariants of Picard curves of genus 3 with complex multiplication. Unlike earlier bounds in genus 2 and 3, our bound is…
Plane quartics over with complex multiplication
Pınar Kılıçer, Hugo Labrande, Reynald Lercier +3
We give examples of smooth plane quartics over with complex multiplication over by a maximal order with primitive CM type. We describe the requ…
Schertz style class invariants for higher degree CM fields
Andreas Enge, Marco Streng
Special values of Siegel modular functions for generate class fields of CM fields. They also yield abelian varieties with a known endomorphism ring…
A bound on the primes of bad reduction for CM curves of genus 3
Pınar Kılıçer, Kristin Lauter, Elisa Lorenzo García +3
We give bounds on the primes of geometric bad reduction for curves of genus three of primitive CM type in terms of the CM orders. In the case of genus one, there are no primes of g…
The CM class number one problem for curves of genus
Pinar Kilicer, Marco Streng
The CM class number one problem for elliptic curves asked to find all elliptic curves defined over the rationals with non-trivial endomorphism ring. For genus-2 curves it is the pr…
Generators of the group of modular units for Gamma1(N) over the rationals
Marco Streng
We give two explicit sets of generators of the group of invertible regular functions over QQ on the modular curve Y1(N). The first set of generators is very surprising. It is essen…
Curves in characteristic 2 with non-trivial 2-torsion
Wouter Castryck, Marco Streng, Damiano Testa
Cais, Ellenberg and Zureick-Brown recently observed that over finite fields of characteristic two, all sufficiently general smooth plane projective curves of a given odd degree adm…
Examples of CM curves of genus two defined over the reflex field
Florian Bouyer, Marco Streng
In "Proving that a genus 2 curve has complex multiplication", van Wamelen lists 19 curves of genus two over with complex multiplication (CM). For each of the 19 curves…
On polarised class groups of orders in quartic CM-fields
Gaetan Bisson, Marco Streng
We give an explicit necessary condition for pairs of orders in a quartic CM-field to have the same polarised class group. This generalises a simpler result for imaginary quadratic…
An explicit version of Shimura's reciprocity law for Siegel modular functions
Marco Streng
We give an explicit version of Shimura's reciprocity law for singular values of Siegel modular functions. We use this to construct the first examples of class invariants of quartic…
Abelian surfaces admitting an (l,l)-endomorphism
Reinier Broker, Kristin Lauter, Marco Streng
We give a classification of all principally polarized abelian surfaces that admit an -isogeny to themselves, and show how to compute all the abelian surfaces that occur. We…
Algebraic divisibility sequences over function fields
Patrick Ingram, Valéry Mahé, Joseph H. Silverman +2
We study the existence of primes and of primitive divisors in classical divisibility sequences defined over function fields. Under various hypotheses, we prove that Lucas sequences…
Computing Igusa class polynomials
Marco Streng
We bound the running time of an algorithm that computes the genus-two class polynomials of a primitive quartic CM-field K. This is in fact the first running time bound and even the…
A CM construction for curves of genus 2 with p-rank 1
Laura Hitt O'Connor, Gary McGuire, Michael Naehrig +1
We construct Weil numbers corresponding to genus-2 curves with -rank 1 over the finite field $\F_{p^2}$ of elements. The corresponding curves can be constructed using expl…
Abelian Varieties with Prescribed Embedding Degree
David Freeman, Peter Stevenhagen, Marco Streng
We present an algorithm that, on input of a CM-field , an integer , and a prime , constructs a -Weil number corresponding to an ordinary…