Specialization at T = 282/31 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -197025213169039645478907T^8 - 341931841726476599360316T^7 + 665947206984249248496984T^6 + 768079108867411834646148T^5 - 206522586961384218063030T^4 + 567964478469951746923788T^3 - 1467887770507529603462256T^2 - 589605913192300591575636T - 60265701752223364133607,
A6 = 36494962374013345038748480651016406T^12 + 110908265109200423180608249500271092T^11 - 159142246935958461715703643687536484T^10 - 720270176428343092357105513183159380T^9 + 221065402893902851082492835239899950T^8 + 1953863404097225126588131072937056920T^7 - 202924758161403130921394088084358680T^6 - 2477568108201452732342173930140320280T^5 + 261194239478925852479287144045333650T^4 + 771382032898538394406350724439690100T^3 + 379387733802661108189747796000121180T^2 + 80405723305695990012919388855834220T + 5982031282168624025426587018231050.
It is a 2-neighbour of the fibration given in curve#3900: its Mordell-Weil lattice (rank 17, no reducible fibres) is a root-free Kneser 2-neighbour of that fibration's, realised by the pencil |O + P - F| for a section P of height 12. Constructed and searched by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.
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