The modular curve $X_{195i}$

Curve name $X_{195i}$
Index $96$
Level $8$
Genus $0$
Does the subgroup contain $-I$? No
Generating matrices $ \left[ \begin{matrix} 7 & 7 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 6 \\ 0 & 7 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $12$ $X_{27}$
Meaning/Special name
Chosen covering $X_{195}$
Curves that $X_{195i}$ minimally covers
Curves that minimally cover $X_{195i}$
Curves that minimally cover $X_{195i}$ and have infinitely many rational points.
Model $\mathbb{P}^{1}$, a universal elliptic curve over an appropriate base is given by \[y^2 = x^3 + A(t)x + B(t), \text{ where}\] \[A(t) = -110592t^{24} + 1714176t^{20} - 1762560t^{16} + 670464t^{12} - 110160t^{8} + 6696t^{4} - 27\] \[B(t) = 14155776t^{36} + 435290112t^{32} - 1252786176t^{28} + 1164312576t^{24} - 529846272t^{20} + 132461568t^{16} - 18192384t^{12} + 1223424t^{8} - 26568t^{4} - 54\]
Info about rational points
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 + xy = x^3 - x^2 + 315x + 1066$, with conductor $45$
Generic density of odd order reductions $299/2688$

Back to the 2-adic image homepage.