Generators and integral points on certain quartic curves
In this paper, we study integral points and generators on quartic curves of the forms u2 ± v4=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 th...
| Permalink: | http://skupni.nsk.hr/Record/nsk.NSK01001075552/Details |
|---|---|
| Matična publikacija: |
Glasnik matematički (Online) 54 (2019), 2 ; str. 321-343 |
| Glavni autori: | Fujita, Yasutsugu (Author), Nara, Tadahisa |
| Vrsta građe: | e-članak |
| Jezik: | eng |
| Predmet: | |
| Online pristup: |
https://doi.org/10.3336/gm.54.2.04 Glasnik matematički (Online) Hrčak |
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| 080 | 1 | |a 51 |2 2011 | |
| 100 | 1 | |a Fujita, Yasutsugu |4 aut | |
| 245 | 1 | 0 | |a Generators and integral points on certain quartic curves |h [Elektronička građa] / |c Yasutsugu Fujita, Tadahisa Nara. |
| 504 | |a Bibliografija: 11 jed. | ||
| 504 | |a Abstract. | ||
| 520 | |a In this paper, we study integral points and generators on quartic curves of the forms u2 ± v4=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. | ||
| 653 | 0 | |a Eliptičke krivulje |a Kvartične krivulje |a Kanonska visina | |
| 700 | 1 | |a Nara, Tadahisa |4 aut |9 HR-ZaNSK | |
| 773 | 0 | |t Glasnik matematički (Online) |x 1846-7989 |g 54 (2019), 2 ; str. 321-343 |w nsk.(HR-ZaNSK)000659858 | |
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| 856 | 4 | 1 | |y Digitalna.nsk.hr |