Curve name | X368 | ||||||||||||
Index | 48 | ||||||||||||
Level | 16 | ||||||||||||
Genus | 2 | ||||||||||||
Does the subgroup contain −I? | Yes | ||||||||||||
Generating matrices | [9941],[111123],[15001],[3003] | ||||||||||||
Images in lower levels |
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Meaning/Special name | |||||||||||||
Chosen covering | X79 | ||||||||||||
Curves that X368 minimally covers | X79 | ||||||||||||
Curves that minimally cover X368 | |||||||||||||
Curves that minimally cover X368 and have infinitely many rational points. | |||||||||||||
Model | y2=−x6+5x4+5x2−1 | ||||||||||||
Info about rational points | No non-singular rational points | ||||||||||||
Comments on finding rational points | The rank of the Jacobian is 0. We use the method of Chabauty. | ||||||||||||
Elliptic curve whose 2-adic image is the subgroup | None | ||||||||||||
Generic density of odd order reductions | N/A |