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 
or 
.
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References
Cremona, J.E.: mwrank and related programs for elliptic curves over Q (1990–2008), http://www.warwick.ac.uk/staff/J.E.Cremona/mwrank/index.html
Cremona, J.E.: Tables of elliptic curves (1990–2008), http://www.warwick.ac.uk/staff/J.E.Cremona/ftp/data/INDEX.html
Silverman, J.H.: Computing heights on elliptic curves. Math. Comp. 51, 339–358 (1988)
Silverman, J.H.: Advanced Topics in the Arithmetic of Elliptic Curves. In: Graduate Texts in Mathematics, vol. 151, Springer, New York (1994)
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Cremona, J.E. (2008). Computing in Component Groups of Elliptic Curves. In: van der Poorten, A.J., Stein, A. (eds) Algorithmic Number Theory. ANTS 2008. Lecture Notes in Computer Science, vol 5011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79456-1_7
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DOI: https://doi.org/10.1007/978-3-540-79456-1_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79455-4
Online ISBN: 978-3-540-79456-1
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