Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Non-hyperelliptic modular Jacobians of dimension 3
HTML articles powered by AMS MathViewer

by Roger Oyono PDF
Math. Comp. 78 (2009), 1173-1191 Request permission


We present a method to solve in an efficient way the problem of constructing the curves given by Torelli’s theorem in dimension $3$ over the complex numbers: For an absolutely simple principally polarized abelian threefold $A$ over $\mathbb {C}$ given by its period matrix $\Omega ,$ compute a model of the curve of genus three (unique up to isomorphism) whose Jacobian, equipped with its canonical polarization, is isomorphic to $A$ as a principally polarized abelian variety. We use this method to describe the non-hyperelliptic modular Jacobians of dimension 3. We investigate all the non-hyperelliptic new modular Jacobians $\textrm {Jac}(C_f)$ of dimension $3$ which are isomorphic to $A_f$, where $f\in S_2^\textrm {new}(X_0 (N)),$ $N\leq 4000.$
Similar Articles
Additional Information
  • Roger Oyono
  • Affiliation: Équipe GAATI, Université de Polynésie Française, BP 6570, 98702 Faa’a, Tahiti, Polynésie Française
  • Email:
  • Received by editor(s): February 5, 2007
  • Received by editor(s) in revised form: March 5, 2008
  • Published electronically: September 3, 2008
  • Additional Notes: The research of this paper was done while the author was a Ph.D. student at the Institut für Experimentelle Mathematik (IEM) of the university of Essen under the supervision of Gerhard Frey
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 78 (2009), 1173-1191
  • MSC (2000): Primary 14C34, 14G35; Secondary 11G10, 11F11, 14H42
  • DOI:
  • MathSciNet review: 2476578