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Let $f: W \rightarrow T$ be an elliptic threefold that is a Weierstrassmodel, which is locally defined by $y^2 = x^3 + fx + g$ over $T$, with asingular fiber such that $(f,g,4f^3 + 27g^2)$ vanishes of order $(4,6,12)$ overan isolated point over $T$. Such a fiber can be explicitly resolved to fiberswith smaller vanishing order and the resulting model, $Y$, contains a rationalelliptic surface, $S$, where some sections of $S$ are flopping curves on $Y$.As a consequence of this arithmetic and geometric connection, we are able todescribe some constraints between flops of $Y$ and the properties of theMordell-Weil group of $S$ and $Y$.

Flops and Mordell-Weil group of Elliptic Threefolds with (4,6,12)-singular fibers