The modular curve $X_{215j}$

Curve name $X_{215j}$
Index $96$
Level $16$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 3 & 6 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 8 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 0 & 3 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $6$ $X_{8}$
$4$ $12$ $X_{25}$
$8$ $48$ $X_{96n}$
Meaning/Special name
Chosen covering $X_{215}$
Curves that $X_{215j}$ minimally covers
Curves that minimally cover $X_{215j}$
Curves that minimally cover $X_{215j}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -108t^{24} - 864t^{20} + 13824t^{12} - 221184t^{4} - 442368\] \[B(t) = -432t^{36} - 5184t^{32} - 10368t^{28} + 96768t^{24} + 663552t^{20} + 2654208t^{16} + 6193152t^{12} - 10616832t^{8} - 84934656t^{4} - 113246208\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + x^2 - 8033x - 275937$, with conductor $4800$
Generic density of odd order reductions $271/2688$

Back to the 2-adic image homepage.