## The modular curve $X_{181f}$

Curve name $X_{181f}$
Index $96$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 5 & 0 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 2 \\ 0 & 5 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $24$ $X_{25h}$
Meaning/Special name
Chosen covering $X_{181}$
Curves that $X_{181f}$ minimally covers
Curves that minimally cover $X_{181f}$
Curves that minimally cover $X_{181f}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -452984832t^{16} - 452984832t^{14} - 84934656t^{12} + 7077888t^{10} - 25436160t^{8} + 110592t^{6} - 20736t^{4} - 1728t^{2} - 27$ $B(t) = -3710851743744t^{24} - 5566277615616t^{22} - 2435246456832t^{20} - 202937204736t^{18} + 508248981504t^{16} + 236458082304t^{14} - 14665383936t^{12} + 3694657536t^{10} + 124084224t^{8} - 774144t^{6} - 145152t^{4} - 5184t^{2} - 54$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - x^2 - 1824x + 25344$, with conductor $816$
Generic density of odd order reductions $215/2688$