Specialization at T = -17/6 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -8119975752906226977600T^8 - 1194538691861755286400T^7 + 219976811381682897431760T^6 - 49925350881736309262160T^5 - 1248367217121272445713640T^4 + 42719940029390047184160T^3 - 7362052252021663964833680T^2 + 3955863107039743188539640T - 544141552392814497282747,
A6 = 282182893507153887108094699833600T^12 - 11546382575277829802734094085120T^11 - 12273663226673659961035941448765824T^10 + 9352497458874682475994018102531840T^9 + 214230436526747031631353358441831440T^8 - 290221811656176148412922343520902080T^7 - 2019839055988652407823845249198695600T^6 + 3106997112557759768822749232574054288T^5 + 9666695459486253875229535486519037880T^4 - 11155397666701195302119070647130234720T^3 + 6035354692251791096533770030129284160T^2 - 1576354013101030906327133713272549480T + 150532543779277207373688778588868886.
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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