There are many references. See e.g. - Barth Peters Hulek Van de Ven Compact complex surfaces - Silverman Advanced topics in the arithmetic of elliptic curves (look foor Tate's algorithm) - Tate, Algorithm for determining the type of a singular fiber in an elliptic pencil. In Modular functions of one variable, IV. - Miranda, The basic theory of elliptic surfaces (This book is hard to find) Note that an A_1 fiber is either a fiber of type II or of type I_1 in Kodaira's notation
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Remke KloostermanMar 16 '11 at 6:30

Remke, your comment looks useful enough to be an answer.
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S. Carnahan♦Mar 16 '11 at 9:38