The modular curve $X_{61c}$

Curve name $X_{61c}$
Index $48$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 3 & 6 \\ 2 & 5 \end{matrix}\right], \left[ \begin{matrix} 1 & 2 \\ 6 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 2 \\ 6 & 5 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $6$ $X_{8}$
$4$ $12$ $X_{24}$
Meaning/Special name
Chosen covering $X_{61}$
Curves that $X_{61c}$ minimally covers
Curves that minimally cover $X_{61c}$
Curves that minimally cover $X_{61c}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -108t^{16} - 324t^{12} - 432t^{8} - 324t^{4} - 108\] \[B(t) = 432t^{24} + 1944t^{20} + 2592t^{16} - 2592t^{8} - 1944t^{4} - 432\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + x^2 - 3722294x + 2761521336$, with conductor $161376$
Generic density of odd order reductions $149/896$

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