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bad reduction

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The Arithmetic of Elliptic Curves 封面

《The Arithmetic of Elliptic Curves》 · 第 196 页 · Chapter VII,Section 5「Good and Bad Reduction」,Definition

Let $E/K$ be an elliptic curve, and let $\widetilde E$ be the reduction modulo $\mathfrak M$ of a minimal Weierstrass equation for $E$. […] $E$ has multiplicative (or semistable) reduction if $\widetilde E$ has a node. $E$ has additive (or unstable) reduction if $\widetilde E$ has a cusp. In cases (b) and (c) we say that $E$ has bad reduction.

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