The modular curve $X_{215f}$

Curve name $X_{215f}$
Index $96$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 7 & 14 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 8 & 7 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $6$ $X_{8}$
$4$ $12$ $X_{25}$
$8$ $48$ $X_{96a}$
Meaning/Special name
Chosen covering $X_{215}$
Curves that $X_{215f}$ minimally covers
Curves that minimally cover $X_{215f}$
Curves that minimally cover $X_{215f}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -108t^{32} + 5184t^{24} - 110592t^{16} + 1327104t^{8} - 7077888\] \[B(t) = 432t^{48} - 31104t^{40} + 663552t^{32} - 169869312t^{16} + 2038431744t^{8} - 7247757312\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - 72300x - 7378000$, with conductor $14400$
Generic density of odd order reductions $51/448$

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