The modular curve $X_{3a}$

Curve name $X_{3a}$
Index $4$
Level $4$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 2 & 3 \\ 3 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 3 & 3 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $1$ $X_{1}$
Meaning/Special name
Chosen covering $X_{3}$
Curves that $X_{3a}$ minimally covers
Curves that minimally cover $X_{3a}$
Curves that minimally cover $X_{3a}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -108t^{6} + 559872t^{4} - 967458816t^{2} + 557256278016\] \[B(t) = 432t^{9} - 2985984t^{7} + 7739670528t^{5} - 8916100448256t^{3} + 3851755393646592t\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy + y = x^3 + 253x - 26862$, with conductor $1058$
Generic density of odd order reductions $179/336$

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