The modular curve $X_{230c}$

Curve name $X_{230c}$
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 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 8 & 7 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $6$ $X_{13}$
$8$ $48$ $X_{102i}$
Meaning/Special name
Chosen covering $X_{230}$
Curves that $X_{230c}$ minimally covers
Curves that minimally cover $X_{230c}$
Curves that minimally cover $X_{230c}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -442368t^{24} + 4423680t^{22} - 16146432t^{20} + 24993792t^{18} - 12358656t^{16} - 3870720t^{14} + 3787776t^{12} - 967680t^{10} - 772416t^{8} + 390528t^{6} - 63072t^{4} + 4320t^{2} - 108\] \[B(t) = 113246208t^{36} - 1698693120t^{34} + 10446962688t^{32} - 33520877568t^{30} + 58350108672t^{28} - 49347035136t^{26} + 7679508480t^{24} + 15967715328t^{22} - 9807298560t^{20} + 2416214016t^{18} - 2451824640t^{16} + 997982208t^{14} + 119992320t^{12} - 192761856t^{10} + 56982528t^{8} - 8183808t^{6} + 637632t^{4} - 25920t^{2} + 432\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - x^2 - 12609x - 1199295$, with conductor $9408$
Generic density of odd order reductions $109/896$

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