## The modular curve $X_{215c}$

Curve name $X_{215c}$
Index $96$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 1 & 0 \\ 8 & 5 \end{matrix}\right], \left[ \begin{matrix} 7 & 14 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $24$ $X_{25n}$ $8$ $48$ $X_{96t}$
Meaning/Special name
Chosen covering $X_{215}$
Curves that $X_{215c}$ minimally covers
Curves that minimally cover $X_{215c}$
Curves that minimally cover $X_{215c}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -27t^{16} + 432t^{8} - 6912$ $B(t) = 54t^{24} - 1296t^{16} - 20736t^{8} + 221184$
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy + y = x^3 + x^2 - 5x + 2$, with conductor $15$
Generic density of odd order reductions $19/336$