## The modular curve $X_{235k}$

Curve name $X_{235k}$
Index $96$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 9 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $6$ $X_{13}$ $8$ $48$ $X_{102m}$
Meaning/Special name
Chosen covering $X_{235}$
Curves that $X_{235k}$ minimally covers
Curves that minimally cover $X_{235k}$
Curves that minimally cover $X_{235k}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -108t^{16} + 864t^{14} - 1296t^{12} - 864t^{10} + 1080t^{8} - 864t^{6} - 1296t^{4} + 864t^{2} - 108$ $B(t) = 432t^{24} - 5184t^{22} + 18144t^{20} - 12096t^{18} - 24624t^{16} + 31104t^{14} + 12096t^{12} + 31104t^{10} - 24624t^{8} - 12096t^{6} + 18144t^{4} - 5184t^{2} + 432$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - x^2 + 13439x + 447361$, with conductor $6720$
Generic density of odd order reductions $299/2688$