Curve name | $X_{339}$ | ||||||||||||
Index | $48$ | ||||||||||||
Level | $16$ | ||||||||||||
Genus | $1$ | ||||||||||||
Does the subgroup contain $-I$? | Yes | ||||||||||||
Generating matrices | $ \left[ \begin{matrix} 3 & 3 \\ 8 & 3 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 5 & 5 \\ 0 & 3 \end{matrix}\right]$ | ||||||||||||
Images in lower levels |
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Meaning/Special name | |||||||||||||
Chosen covering | $X_{85}$ | ||||||||||||
Curves that $X_{339}$ minimally covers | $X_{85}$, $X_{121}$, $X_{168}$ | ||||||||||||
Curves that minimally cover $X_{339}$ | $X_{474}$, $X_{482}$ | ||||||||||||
Curves that minimally cover $X_{339}$ and have infinitely many rational points. | |||||||||||||
Model | A model was not computed. This curve is covered by $X_{168}$, 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 |