Curve name | $X_{642}$ | |||||||||||||||
Index | $96$ | |||||||||||||||
Level | $32$ | |||||||||||||||
Genus | $3$ | |||||||||||||||
Does the subgroup contain $-I$? | Yes | |||||||||||||||
Generating matrices | $ \left[ \begin{matrix} 7 & 0 \\ 0 & 15 \end{matrix}\right], \left[ \begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 7 & 7 \\ 0 & 9 \end{matrix}\right], \left[ \begin{matrix} 7 & 7 \\ 24 & 15 \end{matrix}\right], \left[ \begin{matrix} 5 & 10 \\ 0 & 9 \end{matrix}\right]$ | |||||||||||||||
Images in lower levels |
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Meaning/Special name | ||||||||||||||||
Chosen covering | $X_{340}$ | |||||||||||||||
Curves that $X_{642}$ minimally covers | $X_{340}$ | |||||||||||||||
Curves that minimally cover $X_{642}$ | ||||||||||||||||
Curves that minimally cover $X_{642}$ 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 |