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Computing in component groups of elliptic curves
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Cremona, J. E. (2008) Computing in component groups of elliptic curves. In: 8th International Symposium on Algorithmic Number Theory, Banff, Canada, May 17-22, 2008. Published in: Algorithmic number theory : 8th international symposium, ANTS-VIII, Banff, Canada, May 17-22, 2008 : proceedings (Lecture Notes in Computer Science), Vol.5011 pp. 118-124. ISBN 978-3-540-79455-4. doi:10.1007/978-3-540-79456-1_7 ISSN 0302-9743.
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Abstract
Let K be a p-adic local field and E an elliptic curve defined over K. The component group of E is the group E(K)/E-0(K), where E-0(K) denotes the subgroup of points of good reduction; this is known to be finite, cyclic if E has multiplicative reduction, and of order at most 4 if E has additive reduction. We show how to compute explicitly an isomorphism E(K)/E-0(K) congruent to Z/NZ or E(K)/E-0(K) congruent to Z/2Z x Z/2Z.
| Item Type: | Conference Item (UNSPECIFIED) | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Curves, Elliptic, Group schemes (Mathematics), Computer science -- Mathematics | ||||
| Journal or Publication Title: | Algorithmic number theory : 8th international symposium, ANTS-VIII, Banff, Canada, May 17-22, 2008 : proceedings (Lecture Notes in Computer Science) | ||||
| Publisher: | Springer | ||||
| ISBN: | 978-3-540-79455-4 | ||||
| ISSN: | 0302-9743 | ||||
| Editor: | VanDerPoorten, AJ and Stein, A | ||||
| Official Date: | 2008 | ||||
| Dates: |
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| Volume: | Vol.5011 | ||||
| Number of Pages: | 7 | ||||
| Page Range: | pp. 118-124 | ||||
| DOI: | 10.1007/978-3-540-79456-1_7 | ||||
| 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 |
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