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doctoral thesis
Mordell-Weilove grupe i izogenije familija eliptičkih krivulja
Zagreb: University of Zagreb, Faculty of Science, 2014. urn:nbn:hr:217:252457
Mikić, Miljen
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Mikić, M. (2014). Mordell-Weilove grupe i izogenije familija eliptičkih krivulja (Doctoral thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:252457

Mikić, Miljen. "Mordell-Weilove grupe i izogenije familija eliptičkih krivulja." Doctoral thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:252457

Mikić, Miljen. "Mordell-Weilove grupe i izogenije familija eliptičkih krivulja." Doctoral thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:252457

Mikić, M. (2014). 'Mordell-Weilove grupe i izogenije familija eliptičkih krivulja', Doctoral thesis, University of Zagreb, Faculty of Science, accessed 29 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:252457

Mikić M. Mordell-Weilove grupe i izogenije familija eliptičkih krivulja [Doctoral thesis]. Zagreb: University of Zagreb, Faculty of Science; 2014 [cited 2024 November 29] Available at: https://urn.nsk.hr/urn:nbn:hr:217:252457

M. Mikić, "Mordell-Weilove grupe i izogenije familija eliptičkih krivulja", Doctoral thesis, University of Zagreb, Faculty of Science, Zagreb, 2014. Available at: https://urn.nsk.hr/urn:nbn:hr:217:252457

Metadata
TitleMordell-Weilove grupe i izogenije familija eliptičkih krivulja
Title (english)Mordell-Weil groups and isogenies of the families of elliptic curves
AuthorMiljen Mikić
MentorAndrej Dujella (mentor)
MentorFilip Najman (komentor)
Committee memberIvica Gusić (predsjednik povjerenstva)
Committee memberAndrej Dujella (član povjerenstva)
Committee memberFilip Najman (član povjerenstva)
Committee memberAlan Filipin (član povjerenstva)
Committee memberMatija Kazalicki (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2014-12-02, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Universal decimal classification
(UDC)		51 - Mathematics
Abstract
U ovom radu dokazano je da torzijska grupa eliptičkih krivulja induciranih \(D(4)\)-trojkama može biti ili \(\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}\) ili \(\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/6\mathbb{Z}\). Time je ujedno (kao specijalni slučaj) dobiveno i da torzijska grupa eliptičkih krivulja induciranih Diofantovim trojkama može biti jedna od navedenih. Promatrane su i familije eliptičkih krivulja generiranih Diofantovim trojkama oblika \(\{k−1, k+1, c_{l}(k)\}\) te su određeni torzijska grupa i rang (a time i Mordell-Weilova grupa) koje mogu imati takve krivulje za veliki broj vrijednosti od \(k\) i \(l\). Konačno, promatranjem modularnih krivulja \(X_0(n)\) prebrojano je koliko ima eliptičkih krivulja s cikličkom izogenijom stupnja \(n\) nad raznim kvartičnim poljima.
Abstract (english)
In this work it is proved that the torsion group of elliptic curves induced by \(D(4)\)-triples can be either \(\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}\) or \(\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/6\mathbb{Z}\). Therefore, as a special case it is proved that the torsion group of elliptic curves induced by Diophantine triples can be one of these two, as well. Families of elliptic curves induced by Diophantine triples of the form \(\{k−1, k+1, c_{l}(k)\}\) are examined and the possible form of the torsion group and rank (i.e. Mordell-Weil group) of these curves is determined for the large number of values of \(k\) and \(l\). Finally, by studying modular curves \(X_0(n)\) the number of elliptic curves with cyclic isogeny of degree \(n\) over various quartic fields is found.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:252457
Study programmeTitle: Mathematics
Study programme type: university
Study level: postgraduate
Academic / professional title: doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika (doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika)
Type of resourceText
Extentii, 84 str.
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-03-19 10:00:32