The modular curve $X_{225d}$

Curve name $X_{225d}$
Index $96$
Level $32$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 3 & 3 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 16 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 16 & 7 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $6$ $X_{13}$
$8$ $24$ $X_{85}$
$16$ $48$ $X_{225}$
Meaning/Special name
Chosen covering $X_{225}$
Curves that $X_{225d}$ minimally covers
Curves that minimally cover $X_{225d}$
Curves that minimally cover $X_{225d}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -7421703487488t^{24} - 111325552312320t^{22} - 62388694941696t^{20} - 8697308774400t^{18} - 27179089920t^{16} + 163074539520t^{14} + 31369199616t^{12} + 2548039680t^{10} - 6635520t^{8} - 33177600t^{6} - 3718656t^{4} - 103680t^{2} - 108\] \[B(t) = 7782220156096217088t^{36} - 245139934917030838272t^{34} - 505965907336193114112t^{32} - 222158066018559197184t^{30} - 39557085852032040960t^{28} - 837880636923445248t^{26} + 866973714594398208t^{24} + 192637735721238528t^{22} + 21154638078148608t^{20} - 330541219971072t^{16} - 47030697197568t^{14} - 3307242258432t^{12} + 49941577728t^{10} + 36840407040t^{8} + 3232825344t^{6} + 115043328t^{4} + 870912t^{2} - 432\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - 1244172x + 534156784$, with conductor $2880$
Generic density of odd order reductions $73/672$

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