ɪn nˈʌmbɚ θˈiəɹi, ðɪ ˈɛlkiz tɹaɪnˈoʊmɪəl kˈɜːvz ɑːɹ sˈɜːʔn̩ hˌaɪpɚɹɪlˈɪptɪk kˈɜːvz kənstɹˈʌktᵻd baɪ nˈoʊm ˈɛlkiz wˌɪtʃ hæv ðə pɹˈɑːpɚɾi ðæt ɹˈæʃənəl pˈɔɪnts ˌɔn ðˌɛm kˌɔːɹɪspˈɑːnd tə tɹaɪnˈoʊmɪəl pˌɑːlɪnˈoʊmɪəlz ɡˈɪvɪŋ ɐn ɛkstˈɛnʃən ʌv kjˈuː wɪð pɚtˈɪkjʊlɚ ɡˈælwɑː ɡɹˈuːps.
In number theory, the Elkies trinomial curves are certain hyperelliptic curves constructed by Noam Elkies which have the property that rational points on them correspond to trinomial polynomials giving an extension of Q with particular Galois groups.