---
res:
bibo_abstract:
- Let E be an ordinary elliptic curve over a finite field and g be a positive integer.
Under some technical assumptions, we give an algorithm to span the isomorphism
classes of principally polarized abelian varieties in the isogeny class of E⁹
. The varieties are first described as hermitian lattices over (not necessarily
maximal) quadratic orders and then geometrically in terms of their algebraic theta
null point. We also show how to algebraically compute Siegel modular forms of
even weight given as polynomials in the theta constants by a careful choice of
an affine lift of the theta null point. We then use these results to give an algebraic
computation of Serre’s obstruction for principally polarized abelian threefolds
isogenous to E³ and of the Igusa modular form in dimension 4. We illustrate our
algorithms with examples of curves with many rational points over finite fields.
@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Markus
foaf_name: Kirschmer, Markus
foaf_surname: Kirschmer
foaf_workInfoHomepage: http://www.librecat.org/personId=82258
- foaf_Person:
foaf_givenName: Fabien
foaf_name: Narbonne, Fabien
foaf_surname: Narbonne
- foaf_Person:
foaf_givenName: Christophe
foaf_name: Ritzenthaler, Christophe
foaf_surname: Ritzenthaler
- foaf_Person:
foaf_givenName: Damien
foaf_name: Robert, Damien
foaf_surname: Robert
bibo_doi: 10.1090/mcom/3672
bibo_issue: '333'
bibo_volume: 91
dct_date: 2021^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0025-5718
- http://id.crossref.org/issn/1088-6842
dct_language: eng
dct_publisher: American Mathematical Society (AMS)@
dct_subject:
- Applied Mathematics
- Computational Mathematics
- Algebra and Number Theory
dct_title: Spanning the isogeny class of a power of an elliptic curve@
...