Specialization at T = 261/88 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -52356648678628357469952T^8 - 235519746807875124250368T^7 - 24545191841476895540304T^6 + 811577658055960647489456T^5 + 1079198714145333325459320T^4 + 1254987224811203628397824T^3 - 2522642567144527246899024T^2 - 3309712733210337229896792T - 1026058563214366117251627,
A6 = 4825422219471759579683602107703296T^12 + 34580942274254747650686461570052096T^11 + 31234725928512794727685620659061504T^10 - 273042568629290335756659313007525760T^9 - 455151540100143399461517346503626160T^8 + 1043526152788429910684337802802723904T^7 + 1849381307726983593819115896264667824T^6 - 2215248076398208412328290355259090224T^5 - 3463947301549821564345287894913712680T^4 + 637485311836301536434086156313792000T^3 + 3271887185791747167987145751440802304T^2 + 1998129610230740561490595569733249224T + 403271364874736900390724325685972646.
It is a 2-neighbour of the fibration given in curve#4647: 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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