Nonsolvable polynomials with field discriminant 5a

David P. Roberts

    Research output: Contribution to journalArticlepeer-review

    2 Scopus citations


    We present the first explicitly known polynomials in Z[x] with nonsolvable Galois group and field discriminant of the form ±pA for p ≤ 7 a prime. Our main polynomial has degree 25, Galois group of the form PSL 2(5)5.10, and field discriminant 569. A closely related polynomial has degree 120, Galois group of the form SL 2(5)5.20, and field discriminant 5311. We completely describe 5-adic behavior, finding in particular that the root discriminant of both splitting fields is 125 · 5-1/12500 ≈ 124.984 and the class number of the latter field is divisible by 54.

    Original languageEnglish (US)
    Pages (from-to)289-322
    Number of pages34
    JournalInternational Journal of Number Theory
    Issue number2
    StatePublished - Mar 2011


    • Nonsolvable
    • discriminant
    • number field
    • polynomial
    • ramification

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