Specialization at T = 458/1105 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -1104083919542990740672T^8 - 10725368859924614083328T^7 + 27233182276536009979376T^6 + 206542082020468176713536T^5 - 397181427596358623750980T^4 + 4843779804480200729063344T^3 - 16606432570794981193216279T^2 - 25584496459329575271150212T - 11348709459926316525508132,
A6 = 12350516786472668766297337795840T^12 + 221799272750803971404191627025920T^11 + 569212223298482978503626062159360T^10 - 11869075609185296079185311651020800T^9 - 53903362742072871161532361492760160T^8 + 383972047913208585082616093455327680T^7 + 1230371364926344316718891951621143520T^6 - 7765129801662673724018170759694598720T^5 - 1399242604874728526040920920131327735T^4 + 17367237161504277326036112974588085430T^3 + 57428692355319025444778734345548537226T^2 + 49825188772368199520084299618572523256T + 14830879968852803906439396097627134769.
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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