Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

Explicit isogenies of elliptic curves

Tools
- Tools
+ Tools

Tsukazaki, Kiminori (2013) Explicit isogenies of elliptic curves. PhD thesis, University of Warwick.

[img]
Preview
Text
WRAP_THESIS_Tsukazaki_2013.pdf - Submitted Version

Download (784Kb) | Preview
Official URL: http://webcat.warwick.ac.uk/record=b2688905~S1

Request Changes to record.

Abstract

Let E be an elliptic curve defined over a field K. The main topic of this
thesis is to present a method for the explicit computation of all separable K-
rational l-isogenies of E and isogenous curves for small primes l. The key tool
for this explicit computation is that the modular curve X0(l) parametrises l-
isogenies of elliptic curves. In [3], Cremona and Watkins give explicit isogeny
formulae for l 2 f2; 3; 5; 7; 13g, where the modular curve X0(l) has genus 0.
Their formula allow us to compute l-isogenies of E by simply substituting its
j-invariant and twisting parameter into the formulae. We extend the work
of Cremona and Watkins to the cases l 2 f11; 17; 19; 23; 29; 31; 41; 47; 59; 71g,
where the genus of X0(l) is greater than 0 but the modular curve X+
0 (l) has
genus 0.

Item Type: Thesis or Dissertation (PhD)
Subjects: Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH): Curves, Elliptic, Modular curves
Official Date: July 2013
Dates:
DateEvent
July 2013Submitted
Institution: University of Warwick
Theses Department: Mathematics Institute
Thesis Type: PhD
Publication Status: Unpublished
Supervisor(s)/Advisor: Cremona, J. E.
Sponsors: University of Warwick. Mathematics Institute
Extent: v, 112 leaves.
Language: eng

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics

twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us