The modular curve $X_{230a}$

Curve name $X_{230a}$
Index $96$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 3 & 0 \\ 8 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 8 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 8 & 7 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $6$ $X_{13}$
$8$ $48$ $X_{102m}$
Meaning/Special name
Chosen covering $X_{230}$
Curves that $X_{230a}$ minimally covers
Curves that minimally cover $X_{230a}$
Curves that minimally cover $X_{230a}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -27648t^{16} + 110592t^{14} - 82944t^{12} - 27648t^{10} + 17280t^{8} - 6912t^{6} - 5184t^{4} + 1728t^{2} - 108\] \[B(t) = 1769472t^{24} - 10616832t^{22} + 18579456t^{20} - 6193152t^{18} - 6303744t^{16} + 3981312t^{14} + 774144t^{12} + 995328t^{10} - 393984t^{8} - 96768t^{6} + 72576t^{4} - 10368t^{2} + 432\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + x^2 - 257x + 3423$, with conductor $1344$
Generic density of odd order reductions $271/2688$

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