## The modular curve $X_{233a}$

Curve name $X_{233a}$
Index $96$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 5 & 0 \\ 8 & 5 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 8 & 3 \end{matrix}\right]$
Images in lower levels
 Level Index of image Corresponding curve $2$ $3$ $X_{6}$ $4$ $12$ $X_{13f}$ $8$ $48$ $X_{78i}$
Meaning/Special name
Chosen covering $X_{233}$
Curves that $X_{233a}$ minimally covers
Curves that minimally cover $X_{233a}$
Curves that minimally cover $X_{233a}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -452984832t^{16} - 14042529792t^{14} - 25565331456t^{12} - 14219476992t^{10} - 2838896640t^{8} - 222179328t^{6} - 6241536t^{4} - 53568t^{2} - 27$ $B(t) = 3710851743744t^{24} - 228217382240256t^{22} - 1254151925268480t^{20} - 1946776605032448t^{18} - 1331979249254400t^{16} - 444630885728256t^{14} - 76481562673152t^{12} - 6947357589504t^{10} - 325190246400t^{8} - 7426363392t^{6} - 74753280t^{4} - 212544t^{2} + 54$
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy = x^3 - 27744x - 1781010$, with conductor $102$
Generic density of odd order reductions $53/896$