Specialization at T = -159/26 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -1372222876353130936512T^8 + 45268756700642132762880T^7 - 453891857520504970746000T^6 - 18572366977872800377824T^5 - 1977700547530427488113780T^4 - 1507927812614917602109344T^3 + 3528535081023240424639497T^2 + 739749873585389019295698T - 1838633851571299960339827,
A6 = 20363691452208588844425836248320T^12 - 988378436168557724966091861408768T^11 + 15965030664200057535359388315912960T^10 - 108360266161421346549906270794042880T^9 + 467598254108283083435022152559186336T^8 + 1192549643051435746625317280337017856T^7 - 1110484823304716478646019257293024192T^6 - 2091654238173550372318136090501079360T^5 + 2721622409681114022374952201370443921T^4 + 1932785120958781428078049659343305420T^3 - 2684653676111216975923215434658050073T^2 - 583595531728434724891836911712239106T + 959603028788038989675020832528690546.
It is a 2-neighbour of another fibration built here (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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