Specialization at T = 1815/788 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -28627871103769984370352T^8 + 250727503810391437739328T^7 - 288854657346414564166464T^6 - 1046563569239575640345856T^5 - 2237723908977579748622280T^4 - 2929539083122814891913864T^3 - 75441235775660299609524T^2 + 875991646929384189258912T - 320782968880211172761712,
A6 = 1174522160214039703024876049652096T^12 - 16131442871155893431215736050050816T^11 + 93303642018533859944970389927921664T^10 - 231262072230896017869661906694261760T^9 - 366595866204221333220660871885856160T^8 + 1809536503795113401754131369092034592T^7 + 3099112034539070371703903967203738928T^6 + 554652868729364853437329955292672288T^5 - 394633275566228428167096479633610540T^4 + 857804045527423469286999564571793520T^3 + 199633165297674561155987038442283696T^2 - 284106783901779659207593408557902976T + 70103120599376154084348899681491584.
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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