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

Curve name $X_{235e}$
Index $96$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 7 & 7 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 9 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $6$ $X_{13}$ $8$ $48$ $X_{102i}$
Meaning/Special name
Chosen covering $X_{235}$
Curves that $X_{235e}$ minimally covers
Curves that minimally cover $X_{235e}$
Curves that minimally cover $X_{235e}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -108t^{24} + 2160t^{22} - 15768t^{20} + 48816t^{18} - 48276t^{16} - 30240t^{14} + 59184t^{12} - 30240t^{10} - 48276t^{8} + 48816t^{6} - 15768t^{4} + 2160t^{2} - 108$ $B(t) = 432t^{36} - 12960t^{34} + 159408t^{32} - 1022976t^{30} + 3561408t^{28} - 6023808t^{26} + 1874880t^{24} + 7796736t^{22} - 9577440t^{20} + 4719168t^{18} - 9577440t^{16} + 7796736t^{14} + 1874880t^{12} - 6023808t^{10} + 3561408t^{8} - 1022976t^{6} + 159408t^{4} - 12960t^{2} + 432$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + x^2 + 658495x - 154761825$, with conductor $47040$
Generic density of odd order reductions $271/2688$