The modular curve $X_{93}$

Curve name $X_{93}$
Index $24$
Level $8$
Genus $0$
Does the subgroup contain $-I$? Yes
Generating matrices $ \left[ \begin{matrix} 3 & 6 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 1 \\ 6 & 3 \end{matrix}\right]$
Images in lower levels
LevelIndex of imageCorresponding curve
$2$ $3$ $X_{6}$
$4$ $6$ $X_{12}$
Meaning/Special name
Chosen covering $X_{30}$
Curves that $X_{93}$ minimally covers $X_{30}$
Curves that minimally cover $X_{93}$ $X_{244}$, $X_{265}$, $X_{293}$, $X_{295}$, $X_{296}$, $X_{298}$
Curves that minimally cover $X_{93}$ and have infinitely many rational points. $X_{295}$
Model \[\mathbb{P}^{1}, \mathbb{Q}(X_{93}) = \mathbb{Q}(f_{93}), f_{30} = \frac{f_{93}^{2} - 2}{f_{93} + 1}\]
Info about rational points None
Comments on finding rational points None
Elliptic curve whose $2$-adic image is the subgroup $y^2 = x^3 + x^2 - 355x + 2354$, with conductor $4056$
Generic density of odd order reductions $137/448$

Back to the 2-adic image homepage.