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Published in:
2008 | OriginalPaper | Chapter
Computing in Component Groups of Elliptic Curves
Author : J. E. Cremona
Published in: Algorithmic Number Theory
Publisher: Springer Berlin Heidelberg
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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
.