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The modular curve X677

Curve name X677
Index 96
Level 32
Genus 5
Does the subgroup contain I? Yes
Generating matrices [25081],[23501],[131323],[111101]
Images in lower levels
LevelIndex of imageCorresponding curve
2 3 X6
4 6 X11
8 24 X91
16 48 X291
Meaning/Special name
Chosen covering X291
Curves that X677 minimally covers X291
Curves that minimally cover X677
Curves that minimally cover X677 and have infinitely many rational points.
Model y2=x32xw2=4x2y4xyy3
Info about rational points
Rational pointImage on the j-line
(0:0:1:0) Singular
(0:0:0:1) Singular
Comments on finding rational points This curve admits a family of twists of etale double covers that are also modular curves. Each of these modular curves maps to one we have already computed that has finitely many rational points.
Elliptic curve whose 2-adic image is the subgroup None
Generic density of odd order reductions N/A

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