Iterations of Endomorphisms for 4-Torsion Subgroups of Elliptic Curve

Yutong Fan; Chi Young Ahn; Daeyeoul Kim

doi:10.1002/mma.70836

Iterations of Endomorphisms for 4-Torsion Subgroups of Elliptic Curve

Yutong Fan
, Chi Young Ahn
, Daeyeoul Kim^*

^*Corresponding author for this work

Department of Mathematics

Jeonbuk National University
National Institute for Mathematical Sciences

Research output: Contribution to journal › Journal article › peer-review

Abstract

In this article, we consider sequences generated by iterated matrix multiplication, and introduce a classification of stable, amicable pair, and sociable matrix sequences. Based on these classifications, we analyze the behavior of subgroup sequences obtained through iterated endomorphism on the 4-torsion subgroups of elliptic curves. In addition, we present visual interpretations of these iterations, including symmetric patterns such as four-leaf clovers.

Original language	English
Pages (from-to)	15696-15729
Number of pages	34
Journal	Mathematical Methods in the Applied Sciences
Volume	49
Issue number	14
DOIs	https://doi.org/10.1002/mma.70836
State	Published - 2026.09.30

Keywords

4-torsion subgroups of elliptic curves
amicable pair
homomorphism
iteration
sociable

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10.1002/mma.70836

Cite this

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abstract = "In this article, we consider sequences generated by iterated matrix multiplication, and introduce a classification of stable, amicable pair, and sociable matrix sequences. Based on these classifications, we analyze the behavior of subgroup sequences obtained through iterated endomorphism on the 4-torsion subgroups of elliptic curves. In addition, we present visual interpretations of these iterations, including symmetric patterns such as four-leaf clovers.",

keywords = "4-torsion subgroups of elliptic curves, amicable pair, homomorphism, iteration, sociable",

author = "Yutong Fan and Ahn, \{Chi Young\} and Daeyeoul Kim",

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AU - Fan, Yutong

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Y1 - 2026/9/30

N2 - In this article, we consider sequences generated by iterated matrix multiplication, and introduce a classification of stable, amicable pair, and sociable matrix sequences. Based on these classifications, we analyze the behavior of subgroup sequences obtained through iterated endomorphism on the 4-torsion subgroups of elliptic curves. In addition, we present visual interpretations of these iterations, including symmetric patterns such as four-leaf clovers.

AB - In this article, we consider sequences generated by iterated matrix multiplication, and introduce a classification of stable, amicable pair, and sociable matrix sequences. Based on these classifications, we analyze the behavior of subgroup sequences obtained through iterated endomorphism on the 4-torsion subgroups of elliptic curves. In addition, we present visual interpretations of these iterations, including symmetric patterns such as four-leaf clovers.

KW - 4-torsion subgroups of elliptic curves

KW - amicable pair

KW - homomorphism

KW - iteration

KW - sociable

UR - https://www.scopus.com/pages/publications/105041611441

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DO - 10.1002/mma.70836

M3 - Journal article

AN - SCOPUS:105041611441

SN - 0170-4214

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JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 14

ER -

Iterations of Endomorphisms for 4-Torsion Subgroups of Elliptic Curve

Abstract

Keywords

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