Z/3 K3 family
y^2+(7t^2+309)xy-91(t^2-1)(t^2-25)(t^2-121)y=x^3,
at t=308/87.
Family construction from the Layr-Labs elliptic-rank-challenge-public repository, submission/board/3-r12-z3k3.ec, commit c8f82607a219df846ab80dd9e14ee09a2904d709:
https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/c8f82607a219df846ab80dd9e14ee09a2904d709/submission/board/3-r12-z3k3.ec
This specialization was obtained in the rational-parameter search using the family sections to seed point recovery. The displayed model was independently confirmed globally minimal, and all ten displayed rational points were checked exactly on it. A separate rank computation returned bounds [10,10]; the torsion subgroup is Z/3Z.
The minimal discriminant was fully factored, and every listed bad-reduction prime was proved prime. Attribution for the family construction remains with the cited source.
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