Specialization at T = 31/117 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -80980973155382618456892T^8 + 285465051520066035306000T^7 + 261576072020933408151900T^6 - 951872800330750729557600T^5 - 740266115548451074781940T^4 - 838297434410400458533680T^3 - 2411861402496464207592220T^2 + 321039963467228344391680T - 16364003227722838984000,
A6 = 8727598530781278063259830058307124T^12 - 48350067107354860665788856770508000T^11 + 6795007788217678621771300867414800T^10 + 321740442330556067264524621932532800T^9 - 148612015016082982201355258151421080T^8 - 1249986278690606236857933073188907584T^7 + 185359528793598231769817920929440640T^6 + 3119211110386308385542728766215321280T^5 + 1959126383802129619521972397334285700T^4 - 734642679786885593606821730974577760T^3 + 302738566919351785316592492519057616T^2 - 31992857837231850069180957876807040T + 1040209640416816878466851126534400.
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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