The modular curve $X_{230h}$

Curve name $X_{230h}$
Index $96$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 7 & 7 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 8 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 1 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $12$ $X_{13h}$
$8$ $48$ $X_{102k}$
Meaning/Special name
Chosen covering $X_{230}$
Curves that $X_{230h}$ minimally covers
Curves that minimally cover $X_{230h}$
Curves that minimally cover $X_{230h}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -110592t^{24} + 1105920t^{22} - 4036608t^{20} + 6248448t^{18} - 3089664t^{16} - 967680t^{14} + 946944t^{12} - 241920t^{10} - 193104t^{8} + 97632t^{6} - 15768t^{4} + 1080t^{2} - 27\] \[B(t) = 14155776t^{36} - 212336640t^{34} + 1305870336t^{32} - 4190109696t^{30} + 7293763584t^{28} - 6168379392t^{26} + 959938560t^{24} + 1995964416t^{22} - 1225912320t^{20} + 302026752t^{18} - 306478080t^{16} + 124747776t^{14} + 14999040t^{12} - 24095232t^{10} + 7122816t^{8} - 1022976t^{6} + 79704t^{4} - 3240t^{2} + 54\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy = x^3 - 197x - 2367$, with conductor $294$
Generic density of odd order reductions $81/896$

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