ðiːz ɹˈæʃənəl pˈɔɪnts wɜː pɹˈuːvən baɪ nˈɪlz bɹˈuːɪn jˈuːzɪŋ ðə kəmpjˈuːɾɚ pɹˈoʊɡɹæm kˈæʃ təbi ðɪ ˈoʊnli wˈʌnz ˌɔn sˈiː wˈʌnhˈʌndɹɪd sˈɪksti ˈeɪt, ænd ðeɪ ɡˈɪv ˈoʊnli fˈoːɹ dɪstˈɪŋkt tɹaɪnˈoʊmɪəl pˌɑːlɪnˈoʊmɪəlz wɪð ɡˈælwɑː ɡɹˈuːp pˌiːˌɛsˈɛl tˈuː,sˈɛvən: ˈɛks sˈɛvən dˈæʃ sˈɛvən ˈɛks plˈʌs θɹˈiː ðə tɹˈɪŋks pˌɑːlɪnˈoʊmɪəl, wˈʌn slˈæʃ ɪlˈɛvən ˈɛks sˈɛvən dˈæʃ fˈoːɹtiːn ˈɛks plˈʌs θˈɜːɾi tˈuː ðɪ ˈɜːbɑːxfˈɪʃɚmə kˈeɪ pˌɑːlɪnˈoʊmɪəl ænd tˈuː nˈuː pˌɑːlɪnˈoʊmɪəlz wɪð ɡˈælwɑː ɡɹˈuːp pˌiːˌɛsˈɛl tˈuː,sˈɛvən,
These rational points were proven by Nils Bruin using the computer program Kash to be the only ones on C168, and they give only four distinct trinomial polynomials with Galois group PSL(2,7): x7-7x+3 (the Trinks polynomial), (1/11)x7-14x+32 (the Erbach-Fisher-McKay polynomial) and two new polynomials with Galois group PSL(2,7),