Thongjunthug, Thotsaphon (2008) Computing a lower bound for the canonical height on elliptic curves over totally real number fields. In: 8th International Symposium on Algorithmic Number Theory, Banff, Canada, May 17-22, 2008. Published in: Lecture Notes in Computer Science, Vol.5011 pp. 139-152.

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Abstract

Computing a lower bound for the canonical height is a crucial step in determining a Mordell-Weil basis of an elliptic curve. This paper presents a new algorithm for computing such lower bound, which can be applied to any elliptic curves over totally real number fields. The algorithm is illustrated via some examples.

Item Type:	Conference Item (UNSPECIFIED)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Curves, Elliptic, Numbers, Real
Journal or Publication Title:	Lecture Notes in Computer Science
Publisher:	Springer
ISBN:	978-3-540-79455-4
ISSN:	0302-9743
Date:	2008
Volume:	Vol.5011
Number of Pages:	14
Page Range:	pp. 139-152
Identification Number:	10.1007/978-3-540-79456-1_9
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Title of Event:	8th International Symposium on Algorithmic Number Theory
Type of Event:	Conference
Location of Event:	Banff, Canada
Date(s) of Event:	May 17-22, 2008
References:	1. Cohen, H.: A Course in Computational Algebraic Number Theory, Graduate Texts in Mathematics, vol. 138. Springer, Heidelberg (1993) 2. Cohen, H.: Number Theory. vol. 1: tools and Diophantine equations. Graduate Texts in Mathematics, vol. 239. Springer, Heidelberg (2007) 3. Cremona, J.E.: Algorithms for modular elliptic curves, 2nd edn. Cambridge University Press, Cambridge (1997) 4. Cremona, J.E., Prickett, M., Siksek, S.: Height difference bounds for elliptic curves over number fields. J. Number Theory 116, 42–68 (2006) 5. Cremona, J., Siksek, S.: Computing a lower bound for the canonical height on elliptic curves over Q. In: Hess, F., Pauli, S., Pohst, M. (eds.) ANTS 2006. LNCS, vol. 4076, pp. 275–286. Springer, Heidelberg (2006) 6. Hindry, M., Silverman, J.H.: The canonical height and integral points on elliptic curves. Invent. Math. 93, 419–450 (1988) 7. Siksek, S.: Infinite descent on elliptic curves. Rocky Mountain J. Math. 25, 1501– 1538 (1995) 8. Silverman, J.H.: The arithmetic of elliptic curves. Graduate Texts in Mathematics, vol. 106. Springer, Heidelberg (1986) 9. Silverman, J.H.: Computing heights on elliptic curves. Math. Comp. 51, 339–358 (1988)
URI:	http://wrap.warwick.ac.uk/id/eprint/30089

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