ðə kˈɜːv hɐz dʒˈɛnəs tˈuː, ænd sˌoʊ baɪ fˈɔltɪŋz θˈiəɹəm ðɛɹˌɑːɹ ˈoʊnli ɐ fˈaɪnaɪt nˈʌmbɚɹ ʌv ɹˈæʃənəl pˈɔɪnts ˈɔn ɪt.
The curve has genus two, and so by Faltings theorem there are only a finite number of rational points on it.