Curve name | $X_{260}$ | |||||||||
Index | $48$ | |||||||||
Level | $8$ | |||||||||
Genus | $1$ | |||||||||
Does the subgroup contain $-I$? | Yes | |||||||||
Generating matrices | $ \left[ \begin{matrix} 1 & 2 \\ 4 & 5 \end{matrix}\right], \left[ \begin{matrix} 3 & 1 \\ 4 & 5 \end{matrix}\right], \left[ \begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}\right]$ | |||||||||
Images in lower levels |
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Meaning/Special name | ||||||||||
Chosen covering | $X_{70}$ | |||||||||
Curves that $X_{260}$ minimally covers | $X_{70}$, $X_{94}$, $X_{95}$, $X_{97}$, $X_{130}$, $X_{135}$, $X_{143}$ | |||||||||
Curves that minimally cover $X_{260}$ | ||||||||||
Curves that minimally cover $X_{260}$ and have infinitely many rational points. | ||||||||||
Model | A model was not computed. This curve is covered by $X_{54}$, which only has finitely many rational 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 |