Specialization at T = -6/1891 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -26975048530559638402192T^8 - 312966956619947949551760T^7 - 842243888708948190021348T^6 + 562167338991061514848920T^5 - 461942736201433628752680T^4 + 1431271445622423050083968T^3 + 603334350434130915358656T^2 - 986867998885806893128512T - 418274582761882236107952,
A6 = 1451452485240104576307296743782976T^12 + 24581324346135835035118126720145920T^11 + 152392747348176550954751684612771616T^10 + 397210221029004103236543130531121600T^9 + 10829685735288357984444464355358836T^8 - 1893933432491868927718338035329167456T^7 + 859289861319319080984756807841283568T^6 + 1744608022036113544067265254248327200T^5 - 669413043714196611286442553109280544T^4 - 1068656424150865477675382650153889280T^3 + 65017381339639250150552216405922816T^2 + 368098108547413859417253532055609088T + 103576617923784908883415898755916160.
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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