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

Curve name $X_{203e}$
Index $96$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 3 & 0 \\ 4 & 5 \end{matrix}\right], \left[ \begin{matrix} 5 & 2 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 4 & 5 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $24$ $X_{25n}$
Meaning/Special name
Chosen covering $X_{203}$
Curves that $X_{203e}$ minimally covers
Curves that minimally cover $X_{203e}$
Curves that minimally cover $X_{203e}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -452984832t^{16} - 452984832t^{14} - 1783627776t^{12} - 842268672t^{10} - 184688640t^{8} - 13160448t^{6} - 435456t^{4} - 1728t^{2} - 27$ $B(t) = -3710851743744t^{24} - 5566277615616t^{22} + 26787711025152t^{20} + 29020020277248t^{18} + 20599032250368t^{16} + 7085588742144t^{14} + 1169663459328t^{12} + 110712324096t^{10} + 5029060608t^{8} + 110702592t^{6} + 1596672t^{4} - 5184t^{2} - 54$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - x^2 - 27744x + 1787904$, with conductor $816$
Generic density of odd order reductions $215/2688$