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

Curve name $X_{235i}$
Index $96$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 9 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $12$ $X_{13f}$ $8$ $48$ $X_{102o}$
Meaning/Special name
Chosen covering $X_{235}$
Curves that $X_{235i}$ minimally covers
Curves that minimally cover $X_{235i}$
Curves that minimally cover $X_{235i}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -27t^{16} + 216t^{14} - 324t^{12} - 216t^{10} + 270t^{8} - 216t^{6} - 324t^{4} + 216t^{2} - 27$ $B(t) = -54t^{24} + 648t^{22} - 2268t^{20} + 1512t^{18} + 3078t^{16} - 3888t^{14} - 1512t^{12} - 3888t^{10} + 3078t^{8} + 1512t^{6} - 2268t^{4} + 648t^{2} - 54$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - x^2 + 3360x - 57600$, with conductor $1680$
Generic density of odd order reductions $19/336$