Instytut Matematyczny Polskiej Akademii Nauk / pl / Wydawnictwa / Czasopisma IMPAN / Acta Arithmetica / Wszystkie zeszyty

Streszczenie

We determine all trielliptic modular curves $X_1(N)$ over $\mathbb Q$, and construct explicit trielliptic maps from trielliptic $X_1(N)$ to elliptic curves. By using the trielliptic map constructed for $X_1(21)$, we find six non-cuspidal points of $X_1(21)$ defined over the cubic number field $\mathbb Q(\zeta _9)^+$. So the trielliptic map explains the sporadic elliptic curves over $\mathbb Q(\zeta _9)^+$ with 21-torsion found by Najman [Math. Res. Lett. 23 (2016)].