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For an arbitrary del Pezzo surface S, we compute α(S), which is the volume of a certain polytope in the dual of the effective cone of S, using magma and polymake. The constant α(S) appears in Peyre's conjecture for the asymptotic formula for the number of rational points of bounded height on S over number fields.doi:10.1090/s0025-5718-2013-02772-x fatcat:qiqynxyepzfbphs7sawsoolllm