## The modular curve $X_{181c}$

Curve name $X_{181c}$
Index $96$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 3 & 6 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 4 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 2 \\ 0 & 3 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $12$ $X_{25}$
Meaning/Special name
Chosen covering $X_{181}$
Curves that $X_{181c}$ minimally covers
Curves that minimally cover $X_{181c}$
Curves that minimally cover $X_{181c}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -7421703487488t^{24} - 18554258718720t^{22} - 16930761080832t^{20} - 6551972610048t^{18} - 1244802318336t^{16} - 588880281600t^{14} - 242686623744t^{12} - 9201254400t^{10} - 303906816t^{8} - 24993792t^{6} - 1009152t^{4} - 17280t^{2} - 108$ $B(t) = 7782220156096217088t^{36} + 29183325585360814080t^{34} + 44869363087492251648t^{32} + 35992768221945004032t^{30} + 14705660158248222720t^{28} + 678284325128503296t^{26} - 2579309143227629568t^{24} - 1308832253425483776t^{22} - 237053847955046400t^{20} - 12907038149443584t^{18} - 3703966374297600t^{16} - 319539124371456t^{14} - 9839283535872t^{12} + 40428896256t^{10} + 13695713280t^{8} + 523763712t^{6} + 10202112t^{4} + 103680t^{2} + 432$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + x^2 - 2108929x - 972923809$, with conductor $55488$
Generic density of odd order reductions $109/896$