ɪf ðɛɹ ɛɡzˈɪsts ɐ pˈɔɪnt ˈɛks, wˈaɪ ɔnðə pɹədʒˈɛktɪvˌaɪzd kˈɜːv, ðɛɹ ɪz ɐ kˌɔːɹɪspˈɑːndɪŋ pˈɛɹ bˈiː, sˈiː ʌv ɹˈæʃənəl nˈʌmbɚz, sˈʌtʃ ðætðə tɹaɪnˈoʊmɪəl pˌɑːlɪnˈoʊmɪəl ˈiːðɚ fˈæktɚz ɔːɹ hɐz ɡˈælwɑː ɡɹˈuːp pˌiːˌɛsˈɛl tˈuː,sˈɛvən, ðə fˈaɪnaɪt sˈɪmpəl ɡɹˈuːp ʌv ˈɔːɹdɚ wˈʌnhˈʌndɹɪd sˈɪksti ˈeɪt.
If there exists a point (x, y) on the (projectivized) curve, there is a corresponding pair (b, c) of rational numbers, such that the trinomial polynomial either factors or has Galois group PSL(2,7), the finite simple group of order 168.