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In this paper we describe an elementary criterion how to determine supersingular hyperelliptic curves of genus 2, directly using only the given Weierstrass equation. A family of the hyperelliptic curve H =F p of the type v 2 ¼ u 5 þ a and v 2 ¼ u 5 þ au have been studied.doi:10.1016/j.amc.2004.03.030 fatcat:as2ie2jlefbtffbtae3kzii5rq