Curve name | $X_{250}$ | |||||||||
Index | $48$ | |||||||||
Level | $8$ | |||||||||
Genus | $1$ | |||||||||
Does the subgroup contain $-I$? | Yes | |||||||||
Generating matrices | $ \left[ \begin{matrix} 1 & 5 \\ 2 & 7 \end{matrix}\right], \left[ \begin{matrix} 1 & 0 \\ 2 & 3 \end{matrix}\right], \left[ \begin{matrix} 1 & 1 \\ 6 & 7 \end{matrix}\right]$ | |||||||||
Images in lower levels |
|
|||||||||
Meaning/Special name | ||||||||||
Chosen covering | $X_{69}$ | |||||||||
Curves that $X_{250}$ minimally covers | $X_{69}$ | |||||||||
Curves that minimally cover $X_{250}$ | $X_{537}$, $X_{539}$, $X_{540}$, $X_{542}$, $X_{570}$, $X_{575}$, $X_{577}$, $X_{578}$ | |||||||||
Curves that minimally cover $X_{250}$ and have infinitely many rational points. | ||||||||||
Model | A model was not computed. This curve does not have local points. | |||||||||
Info about rational points | ||||||||||
Comments on finding rational points | None | |||||||||
Elliptic curve whose $2$-adic image is the subgroup | None | |||||||||
Generic density of odd order reductions | N/A |