Hessian matrices, automorphisms of $p$-groups, and torsion points of elliptic curves

Stanojkovski M, Voll C (2021)
Mathematische Annalen 381: 593–629.

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Stanojkovski, Mima; Voll, ChristopherUniBi
Abstract / Bemerkung
We describe the automorphism groups of finite p-groups arising naturally via Hessian determinantal representations of elliptic curves defined over number fields. Moreover, we derive explicit formulas for the orders of these automorphism groups for elliptic curves of j-invariant 1728 given in Weierstrass form. We interpret these orders in terms of the numbers of 3-torsion points (or flex points) of the relevant curves over finite fields. Our work greatly generalizes and conceptualizes previous examples given by du Sautoy and Vaughan-Lee. It explains, in particular, why the orders arising in these examples are polynomial on Frobenius sets and vary with the primes in a nonquasipolynomial manner.
Erscheinungsjahr
2021
Zeitschriftentitel
Mathematische Annalen
Band
381
Seite(n)
593–629
ISSN
0025-5831
eISSN
1432-1807
Finanzierungs-Informationen
Open-Access-Publikationskosten wurden durch die Universität Bielefeld im Rahmen des DEAL-Vertrags gefördert.
Page URI
https://pub.uni-bielefeld.de/record/2950122

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Stanojkovski M, Voll C. Hessian matrices, automorphisms of $p$-groups, and torsion points of elliptic curves. Mathematische Annalen. 2021;381:593–629.
Stanojkovski, M., & Voll, C. (2021). Hessian matrices, automorphisms of $p$-groups, and torsion points of elliptic curves. Mathematische Annalen, 381, 593–629. https://doi.org/10.1007/s00208-021-02193-8
Stanojkovski, Mima, and Voll, Christopher. 2021. “Hessian matrices, automorphisms of $p$-groups, and torsion points of elliptic curves”. Mathematische Annalen 381: 593–629.
Stanojkovski, M., and Voll, C. (2021). Hessian matrices, automorphisms of $p$-groups, and torsion points of elliptic curves. Mathematische Annalen 381, 593–629.
Stanojkovski, M., & Voll, C., 2021. Hessian matrices, automorphisms of $p$-groups, and torsion points of elliptic curves. Mathematische Annalen, 381, p 593–629.
M. Stanojkovski and C. Voll, “Hessian matrices, automorphisms of $p$-groups, and torsion points of elliptic curves”, Mathematische Annalen, vol. 381, 2021, pp. 593–629.
Stanojkovski, M., Voll, C.: Hessian matrices, automorphisms of $p$-groups, and torsion points of elliptic curves. Mathematische Annalen. 381, 593–629 (2021).
Stanojkovski, Mima, and Voll, Christopher. “Hessian matrices, automorphisms of $p$-groups, and torsion points of elliptic curves”. Mathematische Annalen 381 (2021): 593–629.
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2022-08-02T08:12:29Z
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arXiv: 1912.09860

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