## The modular curve $X_{60a}$

Curve name $X_{60a}$
Index $48$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 3 & 3 \\ 4 & 5 \end{matrix}\right], \left[ \begin{matrix} 1 & 1 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 3 & 3 \\ 0 & 5 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $24$ $X_{60}$
Meaning/Special name
Chosen covering $X_{60}$
Curves that $X_{60a}$ minimally covers
Curves that minimally cover $X_{60a}$
Curves that minimally cover $X_{60a}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -27648t^{16} + 82944t^{12} + 44928t^{8} + 5184t^{4} - 108$ $B(t) = 1769472t^{24} + 15925248t^{20} + 7630848t^{16} - 476928t^{8} - 62208t^{4} - 432$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + 1300x - 34000$, with conductor $1600$
Generic density of odd order reductions $419/2688$