## The modular curve $X_{203b}$

Curve name $X_{203b}$
Index $96$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 1 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 6 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 3 & 6 \\ 4 & 7 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $24$ $X_{25i}$
Meaning/Special name
Chosen covering $X_{203}$
Curves that $X_{203b}$ minimally covers
Curves that minimally cover $X_{203b}$
Curves that minimally cover $X_{203b}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -1811939328t^{16} - 1811939328t^{14} - 7134511104t^{12} - 3369074688t^{10} - 738754560t^{8} - 52641792t^{6} - 1741824t^{4} - 6912t^{2} - 108$ $B(t) = 29686813949952t^{24} + 44530220924928t^{22} - 214301688201216t^{20} - 232160162217984t^{18} - 164792258002944t^{16} - 56684709937152t^{14} - 9357307674624t^{12} - 885698592768t^{10} - 40232484864t^{8} - 885620736t^{6} - 12773376t^{4} + 41472t^{2} + 432$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - x^2 - 110977x - 14192255$, with conductor $3264$
Generic density of odd order reductions $109/896$