arXiv
Open Access
2017
The divisibility by 2 of rational points on elliptic curves
Boris M. Bekker
Yuri G. Zarhin
Abstrak
We give a simple proof of the well-known divisibility by 2 condition for rational points on elliptic curves with rational 2-torsion. As an application of the explicit division by $2^n$ formulas obtained in Sec.2, we construct versal families of elliptic curves containing points of orders 4, 5, 6, and 8 from which we obtain an explicit description of elliptic curves over certain finite fields $\mathbb{F}_q$ with a prescribed (small) group $E(\mathbb{F}_q)$. In the last two sections we study 3- and 5-torsion. This paper supercedes arXiv:1605.09279 [math.NT] .
Penulis (2)
B
Boris M. Bekker
Y
Yuri G. Zarhin
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2017
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- en
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- arXiv
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- Open Access ✓