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

Curve name $X_{203c}$
Index $96$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 5 & 2 \\ 4 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 4 & 3 \end{matrix}\right], \left[ \begin{matrix} 3 & 6 \\ 4 & 7 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $12$ $X_{25}$
Meaning/Special name
Chosen covering $X_{203}$
Curves that $X_{203c}$ minimally covers
Curves that minimally cover $X_{203c}$
Curves that minimally cover $X_{203c}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -1855425871872t^{24} - 4638564679680t^{22} - 11190537289728t^{20} - 15553687191552t^{18} - 10313105670144t^{16} - 3408710860800t^{14} - 614445613056t^{12} - 53261107200t^{10} - 2517848064t^{8} - 59332608t^{6} - 667008t^{4} - 4320t^{2} - 27$ $B(t) = -972777519512027136t^{36} - 3647915698170101760t^{34} + 2051952580220682240t^{32} + 20397928612267819008t^{30} + 33951265400234704896t^{28} + 30617554940910895104t^{26} + 17785117899497668608t^{24} + 6808203212101779456t^{22} + 1663165831279804416t^{20} + 257577264353378304t^{18} + 25986966113746944t^{16} + 1662158987329536t^{14} + 67844840620032t^{12} + 1824948486144t^{10} + 31619579904t^{8} + 296828928t^{6} + 466560t^{4} - 12960t^{2} - 54$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + x^2 - 8018112x + 8735863860$, with conductor $13872$
Generic density of odd order reductions $299/2688$