Specialization at T = -10/1 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -118937177346945845659707T^8 - 178627984651034750261448T^7 + 538725115408622183167176T^6 + 932687723092640101942896T^5 - 785596976914037914856880T^4 + 532319133790622065220064T^3 - 1885695726240745162373664T^2 - 977032720488720551059872T - 121021369855000800926832,
A6 = 15700020995297278065702962968986006T^12 + 37259362275892277501775777129653976T^11 - 91123084323059325303034614872980296T^10 - 338078840866824691573377389572497840T^9 + 146594450200795609255542798171153120T^8 + 1165683634482625362035291597494076064T^7 + 136953122145599945469132137315051424T^6 - 2655038031228910497864633944351855904T^5 + 509959130847733176223681554198385680T^4 + 1350975024523639142563101930559667520T^3 + 692961598461491245602665065671309504T^2 + 172025669836703204112379176286164864T + 16373121443610735589881083198960256.
It is a 2-neighbour of the fibration given in curve#4205 (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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