## The modular curve $X_{92h}$

Curve name $X_{92h}$
Index $48$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $24$ $X_{27h}$
Meaning/Special name
Chosen covering $X_{92}$
Curves that $X_{92h}$ minimally covers
Curves that minimally cover $X_{92h}$
Curves that minimally cover $X_{92h}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -27t^{8} + 1620t^{6} - 3618t^{4} + 1620t^{2} - 27$ $B(t) = 54t^{12} + 6804t^{10} - 56214t^{8} + 95256t^{6} - 56214t^{4} + 6804t^{2} + 54$
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy = x^3 + 605x - 19750$, with conductor $195$
Generic density of odd order reductions $5/84$