document: Hilbert modular threefolds of arithmetic genus one D. Weisser -LRB- 1981 -RRB- proved that there are exactly four Galois cubic number fields with Hilbert modular threefolds of arithmetic genus one . In this paper , we extend Weisser 's work to cover all cubic number fields . Our main result is that there are exactly 33 fields with Hilbert modular threefolds of arithmetic genus one . These fields are enumerated explicitly
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