The modular curve $X_{234a}$

Curve name $X_{234a}$
Index $96$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $\left[ \begin{matrix} 1 & 1 \\ 8 & 3 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 8 & 5 \end{matrix}\right]$
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 $X_{234}$
Curves that $X_{234a}$ minimally covers
Curves that minimally cover $X_{234a}$
Curves that minimally cover $X_{234a}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by $y^2 = x^3 + A(t)x + B(t), \text{ where}$ $A(t) = -31131t^{16} - 413856t^{15} - 2554848t^{14} - 9991296t^{13} - 26526528t^{12} - 52738560t^{11} - 84865536t^{10} - 77580288t^{9} - 169468416t^{8} + 310321152t^{7} - 1357848576t^{6} + 3375267840t^{5} - 6790791168t^{4} + 10231087104t^{3} - 10464657408t^{2} + 6780616704t - 2040201216$ $B(t) = -2114154t^{24} - 42158880t^{23} - 400357728t^{22} - 2437513344t^{21} - 10602010944t^{20} - 35081786880t^{19} - 91919826432t^{18} - 197139142656t^{17} - 344702449152t^{16} - 507370881024t^{15} - 640018464768t^{14} - 539658878976t^{13} - 1287773061120t^{12} + 2158635515904t^{11} - 10240295436288t^{10} + 32471736385536t^{9} - 88243826982912t^{8} + 201870482079744t^{7} - 376503609065472t^{6} + 574779996241920t^{5} - 694813389225984t^{4} + 638979498049536t^{3} - 419805504995328t^{2} + 176827159019520t - 35469618315264$
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - x^2 - 384x - 2772$, with conductor $24$
Generic density of odd order reductions $215/2688$