Isogeny graphs with maximal real multiplication

DOI10.1016/j.jnt.2019.06.019zbMath1457.11082arXiv1407.6672OpenAlexW2970019229MaRDI QIDQ2329281

Emmanuel Thomé, Sorina Ionica

Publication date: 17 October 2019

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.6672

zbMATH Keywords

algorithmabelian varietycomplex multiplicationreal multiplicationTate pairingendomorphism ring

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Complex multiplication and moduli of abelian varieties (11G15) Isogeny (14K02)

Related Items (3)

Variations in the distribution of principally polarized abelian varieties among isogeny classes ⋮ Isogeny graphs of ordinary abelian varieties ⋮ The structure of the group of rational points of an abelian variety over a finite field

Uses Software

• AVIsogenies

Cites Work

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• The distance between superspecial abelian varieties with real multiplication
• The Weil pairing, and its efficient calculation
• Approximating rings of integers in number fields
• Variétés abeliennes ordinaires sur un corps fini
• Duality theorems for curves over p-adic fields
• Computing Igusa class polynomials
• Computing isogenies between abelian varieties
• Pairing the volcano
• Computing $(\ell ,\ell )$-isogenies in polynomial time on Jacobians of genus $2$ curves
• Computing endomorphism rings of abelian varieties of dimension two
• Another Approach to Pairing Computation in Edwards Coordinates

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