The modular curve $X_{79a}$

Curve name $X_{79a}$
Index $48$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 3 & 3 \\ 4 & 5 \end{matrix}\right], \left[ \begin{matrix} 1 & 3 \\ 4 & 9 \end{matrix}\right], \left[ \begin{matrix} 1 & 1 \\ 4 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 3 \\ 12 & 11 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $6$ $X_{13}$
$8$ $24$ $X_{79}$
Meaning/Special name
Chosen covering $X_{79}$
Curves that $X_{79a}$ minimally covers
Curves that minimally cover $X_{79a}$
Curves that minimally cover $X_{79a}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -891t^{12} - 7452t^{11} - 28944t^{10} - 65880t^{9} - 92340t^{8} - 80352t^{7} - 69120t^{6} - 160704t^{5} - 369360t^{4} - 527040t^{3} - 463104t^{2} - 238464t - 57024\] \[B(t) = -10206t^{18} - 127332t^{17} - 749412t^{16} - 2666736t^{15} - 5957712t^{14} - 6676992t^{13} + 6537888t^{12} + 49180608t^{11} + 125846784t^{10} + 211545216t^{9} + 251693568t^{8} + 196722432t^{7} + 52303104t^{6} - 106831872t^{5} - 190646784t^{4} - 170671104t^{3} - 95924736t^{2} - 32596992t - 5225472\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 - 326675x - 71865750$, with conductor $5600$
Generic density of odd order reductions $9249/57344$

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