## The modular curve $X_{202c}$

Curve name $X_{202c}$
Index $96$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 7 & 0 \\ 8 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 8 & 7 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $6$ $X_{13}$ $8$ $48$ $X_{202}$
Meaning/Special name
Chosen covering $X_{202}$
Curves that $X_{202c}$ minimally covers
Curves that minimally cover $X_{202c}$
Curves that minimally cover $X_{202c}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -110592t^{24} - 12165120t^{22} + 55683072t^{20} + 16201728t^{18} - 276804864t^{16} + 219663360t^{14} - 98585856t^{12} + 54915840t^{10} - 17300304t^{8} + 253152t^{6} + 217512t^{4} - 11880t^{2} - 27$ $B(t) = 14155776t^{36} - 3779592192t^{34} - 7612268544t^{32} + 261570428928t^{30} - 973701513216t^{28} + 1124205723648t^{26} - 307830620160t^{24} + 933830000640t^{22} - 1721116864512t^{20} + 1236216729600t^{18} - 430279216128t^{16} + 58364375040t^{14} - 4809853440t^{12} + 4391428608t^{10} - 950880384t^{8} + 63859968t^{6} - 464616t^{4} - 57672t^{2} + 54$
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy = x^3 - 44787x + 3609423$, with conductor $294$
Generic density of odd order reductions $81/896$