## The modular curve $X_{101o}$

Curve name $X_{101o}$
Index $48$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 1 & 0 \\ 0 & 5 \end{matrix}\right], \left[ \begin{matrix} 7 & 6 \\ 4 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 4 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 4 & 1 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $12$ $X_{25}$
Meaning/Special name
Chosen covering $X_{101}$
Curves that $X_{101o}$ minimally covers
Curves that minimally cover $X_{101o}$
Curves that minimally cover $X_{101o}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -7077888t^{12} + 5308416t^{10} - 1548288t^{8} + 221184t^{6} - 17280t^{4} + 864t^{2} - 27$ $B(t) = 7247757312t^{18} - 8153726976t^{16} + 3906994176t^{14} - 1040449536t^{12} + 164560896t^{10} - 14598144t^{8} + 483840t^{6} + 25920t^{4} - 2592t^{2} + 54$
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy + y = x^3 + x^2 - 2402x + 44246$, with conductor $147$
Generic density of odd order reductions $25/224$