Specialization at T = 434/205 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -5184596861019629847612T^8 - 133754925365232341831388T^7 - 1035437637468603823145739T^6 - 1575565271267685915981924T^5 - 1170680387853697770352680T^4 + 900828146471472012207744T^3 + 1832423192062073064608256T^2 - 1187684595807033661235712T - 1681976130623118064380672,
A6 = 149744321704475419746038421127284T^12 + 5524322875536651418776153811707324T^11 + 73960445444599888122367809067169241T^10 + 447433713175257084856032889546498740T^9 + 1270478308377182851928891301866983125T^8 + 510043107515189769341895147322518288T^7 - 1365617314830659026227384880724910192T^6 + 394471188044464447389716164705234752T^5 + 2190221113813265570364601521374517120T^4 - 625950896394979706215937393243105280T^3 - 1449978984373691606292352028569522176T^2 + 834866943439151412261391613342736384T + 852857001347003013712347074940788736.
It is a 2-neighbour of the fibration given in curve#4191 (itself a 2-neighbour of the fibration 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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