Curve name | $X_{559}$ | ||||||||||||
Index | $96$ | ||||||||||||
Level | $16$ | ||||||||||||
Genus | $3$ | ||||||||||||
Does the subgroup contain $-I$? | Yes | ||||||||||||
Generating matrices | $ \left[ \begin{matrix} 7 & 7 \\ 8 & 7 \end{matrix}\right], \left[ \begin{matrix} 7 & 14 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 5 \\ 0 & 1 \end{matrix}\right]$ | ||||||||||||
Images in lower levels |
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Meaning/Special name | |||||||||||||
Chosen covering | $X_{340}$ | ||||||||||||
Curves that $X_{559}$ minimally covers | $X_{340}$ | ||||||||||||
Curves that minimally cover $X_{559}$ | |||||||||||||
Curves that minimally cover $X_{559}$ 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 |