Specialization at T = -120/121 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -18808819639564736183472T^8 - 270390604164314807890368T^7 - 1064698058908765727554464T^6 - 690609682722857600525472T^5 - 1141985348588431905168240T^4 - 1276711546748486547364128T^3 + 1533178281333365507000016T^2 + 1003847548076768965363668T - 662667526757651887035567,
A6 = 198461588427944563947255082869120T^12 + 5470876228138813326458542895357184T^11 + 78310570892779922090226615255906432T^10 + 585449236963957414662829259015483520T^9 + 1854487489939448014773845858584024704T^8 + 1020492248925323261478020126191388928T^7 - 2397613146941260720543566338947934208T^6 - 1992669351542649345334637022139959408T^5 + 1587582544452083911151305726515006564T^4 + 1461616308592226634206845276455690360T^3 - 684661031717307107294832767505632268T^2 - 464296295429065890603785053139616684T + 208515476578669742594974588404489810.
It is a 2-neighbour of the fibration given in curve#4191 (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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