## The modular curve $X_{242b}$

Curve name $X_{242b}$
Index $96$
Level $32$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 3 & 9 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 7 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $12$ $X_{13f}$ $8$ $24$ $X_{32i}$ $16$ $48$ $X_{116i}$
Meaning/Special name
Chosen covering $X_{242}$
Curves that $X_{242b}$ minimally covers
Curves that minimally cover $X_{242b}$
Curves that minimally cover $X_{242b}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -27t^{16} - 432t^{8} - 432$ $B(t) = -54t^{24} - 1296t^{16} - 6480t^{8} + 3456$
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy + y = x^3 - x^2 - 91x - 310$, with conductor $17$
Generic density of odd order reductions $9827/86016$