The modular curve $X_{235h}$

Curve name $X_{235h}$
Index $96$
Level $32$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 16 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 9 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $6$ $X_{13}$
$8$ $24$ $X_{102}$
$16$ $48$ $X_{235}$
Meaning/Special name
Chosen covering $X_{235}$
Curves that $X_{235h}$ minimally covers
Curves that minimally cover $X_{235h}$
Curves that minimally cover $X_{235h}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -108t^{22} + 1080t^{20} - 3132t^{18} + 2592t^{16} + 1512t^{14} - 3888t^{12} + 1512t^{10} + 2592t^{8} - 3132t^{6} + 1080t^{4} - 108t^{2}\] \[B(t) = 432t^{33} - 6480t^{31} + 34992t^{29} - 82512t^{27} + 71280t^{25} + 50544t^{23} - 142992t^{21} + 112752t^{19} - 112752t^{17} + 142992t^{15} - 50544t^{13} - 71280t^{11} + 82512t^{9} - 34992t^{7} + 6480t^{5} - 432t^{3}\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy = x^3 - x^2 + 1890x - 24300$, with conductor $630$
Generic density of odd order reductions $271/2688$

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