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

Curve name $X_{181a}$
Index $96$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 3 & 6 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 7 & 6 \\ 4 & 3 \end{matrix}\right], \left[ \begin{matrix} 5 & 2 \\ 0 & 3 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $6$ $X_{8}$ $4$ $24$ $X_{25i}$
Meaning/Special name
Chosen covering $X_{181}$
Curves that $X_{181a}$ minimally covers
Curves that minimally cover $X_{181a}$
Curves that minimally cover $X_{181a}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -1855425871872t^{24} - 4638564679680t^{22} - 4232690270208t^{20} - 1637993152512t^{18} - 311200579584t^{16} - 147220070400t^{14} - 60671655936t^{12} - 2300313600t^{10} - 75976704t^{8} - 6248448t^{6} - 252288t^{4} - 4320t^{2} - 27$ $B(t) = 972777519512027136t^{36} + 3647915698170101760t^{34} + 5608670385936531456t^{32} + 4499096027743125504t^{30} + 1838207519781027840t^{28} + 84785540641062912t^{26} - 322413642903453696t^{24} - 163604031678185472t^{22} - 29631730994380800t^{20} - 1613379768680448t^{18} - 462995796787200t^{16} - 39942390546432t^{14} - 1229910441984t^{12} + 5053612032t^{10} + 1711964160t^{8} + 65470464t^{6} + 1275264t^{4} + 12960t^{2} + 54$
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy + y = x^3 + x^2 - 32952x - 1912599$, with conductor $1734$
Generic density of odd order reductions $299/2688$