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.
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.