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https://doi.org/10.3336/gm.54.2.04

Generators and integral points on certain quartic curves

Yasutsugu Fujita   ORCID icon orcid.org/0000-0001-7985-9667 ; College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba 275-8576, Japan
Tadahisa Nara ; Faculty of Engineering, Tohoku-Gakuin University, 1-13-1 Chuo, Tagajo, Miyagi 985-8537, Japan

Puni tekst: engleski, pdf (203 KB) str. 321-343 preuzimanja: 208* citiraj
APA 6th Edition
Fujita, Y. i Nara, T. (2019). Generators and integral points on certain quartic curves. Glasnik matematički, 54 (2), 321-343. https://doi.org/10.3336/gm.54.2.04
MLA 8th Edition
Fujita, Yasutsugu i Tadahisa Nara. "Generators and integral points on certain quartic curves." Glasnik matematički, vol. 54, br. 2, 2019, str. 321-343. https://doi.org/10.3336/gm.54.2.04. Citirano 20.10.2021.
Chicago 17th Edition
Fujita, Yasutsugu i Tadahisa Nara. "Generators and integral points on certain quartic curves." Glasnik matematički 54, br. 2 (2019): 321-343. https://doi.org/10.3336/gm.54.2.04
Harvard
Fujita, Y., i Nara, T. (2019). 'Generators and integral points on certain quartic curves', Glasnik matematički, 54(2), str. 321-343. https://doi.org/10.3336/gm.54.2.04
Vancouver
Fujita Y, Nara T. Generators and integral points on certain quartic curves. Glasnik matematički [Internet]. 2019 [pristupljeno 20.10.2021.];54(2):321-343. https://doi.org/10.3336/gm.54.2.04
IEEE
Y. Fujita i T. Nara, "Generators and integral points on certain quartic curves", Glasnik matematički, vol.54, br. 2, str. 321-343, 2019. [Online]. https://doi.org/10.3336/gm.54.2.04

Sažetak
In this paper, we study integral points and generators on quartic curves of the forms \(u^2 \pm v^4=m\) for a nonzero integer $m$. The main results assert that certain integral points on the curves can be extended to bases for the Mordell-Weil groups of the elliptic curves attached to the quartic curves in the cases where the Mordell-Weil ranks are at most two. As corollaries, we explicitly describe the integral points on the quartic curves in each case where the ranks are one and two.

Ključne riječi
Elliptic curve; quartic curve; canonical height; integral points

Hrčak ID: 229601

URI
https://hrcak.srce.hr/229601

Posjeta: 359 *