Computing in Component Groups of Elliptic Curves

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)/E0(K), where E0(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)/E0(K) = Z/NZ or E(K)/E0(K) = Z/2Z

• Type: Conference
• Year: 2008
• Where: ANTS
• Authors: J. E. Cremona
• Keywords: Algorithms, ANTS 2008, Elliptic Curve, Multiplicative Reduction, P-adic Local Field