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The modular curve X368

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
LevelIndex of imageCorresponding curve
2 3 X6
4 6 X13
8 24 X79
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+5x21
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

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