Specialization at T = -485/27 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -13129724922135998400T^8 - 393315956007325349760T^7 + 5388075614914218900720T^6 + 133624136603638823580000T^5 - 2980942426742659655805540T^4 + 33575588298751816593482040T^3 - 178476287434090182905197255T^2 - 27064681539446356514316710T - 38737534397522382035015527,
A6 = 17001575848734905085648825600T^12 + 808662010058021550277497323520T^11 + 2204274099561464081452163602176T^10 - 450617120852864904310146381112320T^9 - 6041711991147376183046964974244960T^8 + 125500678000542015284784371883062400T^7 + 2667323428245326791597400104572570240T^6 - 56072697432225196572060046394633385120T^5 + 291328099318551627699751437189468287265T^4 - 366248679959978292773278702918063389000T^3 + 804324836109783714230677491953667748735T^2 + 249729199613745513617677147674877497230T + 91023269067533367175532101155650107690.
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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