Computing in Component Groups of Elliptic Curves
نویسنده
چکیده
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× Z/2Z.
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