Specialization at T = -765/779 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -43748288271748043306667T^8 + 231005568889113088943880T^7 - 41811485832351502958160T^6 - 845807620575605275473120T^5 - 1273696848822391714464840T^4 - 2479538071066771770038640T^3 - 723198327599392266394800T^2 + 1473487148401141809248640T - 304202213366895598996800,
A6 = 3496542619563277295766359856805926T^12 - 28800862572418754868158883533967960T^11 + 61983572330491650413223232787176320T^10 + 92074250730656596945854018024980640T^9 - 554403246688053294582105340433199720T^8 + 21665370800800153534189468438161072T^7 + 2696996106708736152461893481712643920T^6 + 2003709311601233451889158133572553920T^5 - 1216187330113512252280500336077191920T^4 - 278472048982945948218206647760751360T^3 + 596780792582732967834659478701644416T^2 - 397452607403627859574187730447221760T + 82758424296652691415712452035078400.
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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