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Explicit isogenies of elliptic curves
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Tsukazaki, Kiminori (2013) Explicit isogenies of elliptic curves. PhD thesis, University of Warwick.
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WRAP_THESIS_Tsukazaki_2013.pdf - Submitted Version Download (784Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b2688905~S1
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 (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Curves, Elliptic, Modular curves | ||||
Official Date: | July 2013 | ||||
Dates: |
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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Publication Status: | Unpublished | ||||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 |
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