Specialization at T = -25/4 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -4261577599459448669952T^8 - 64973986302543234990336T^7 - 520389045926789466560976T^6 + 1345632567339050301405168T^5 - 1166046837124054463831880T^4 + 1467990670474011670789248T^3 + 708396134646378930038064T^2 - 2039012801108036751604536T - 1064612557866595153534587,
A6 = 114526854942132148192119773896704T^12 + 2886461604328553455092851655364608T^11 + 26297663143880669828973879786142464T^10 + 17285767061810088763243303592653440T^9 + 283423484340379516362999699927180240T^8 - 1873846284164641695090670451164046016T^7 + 1691887389529509979005107697145077168T^6 + 2214587379454712720775944886272688144T^5 - 1928086685736271044313072682680488360T^4 - 2342333230882985957665359245249370240T^3 + 626736207616137047035294839823032576T^2 + 1430459043024515641147100607262149672T + 441006788801640809301392680791854166.
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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