Specialization at T = -7/13 of a rank-17 fibration of X1092 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -105011986328338530184252T^8 + 1624598433710275617978304T^7 - 6321400765862790768797668T^6 - 6714644299565372036732264T^5 - 5697585703504986516411400T^4 - 19474800058502498278832768T^3 + 22490650492223580303426560T^2 + 23684368560400255356574528T - 19516759643691525209970352,
A6 = 13613297573190764450387734076665396T^12 - 279747285467910413302835983826594288T^11 + 2042517619565912841517522343157110840T^10 - 6782403520591044024313048723487823440T^9 + 4706947676894032497276227735499747396T^8 + 67181083628538099142151895496763512032T^7 + 7944774490731402629902892096898574128T^6 - 127085975499992571495595833570771036000T^5 + 2577039428202679942233522288128755296T^4 + 133317246010924356002971327979124643840T^3 - 38493179266151915812989454964700702464T^2 - 65224947674167075345316672819115241216T + 33481436299182969940397985534717172096.
It is a 2-neighbour of the fibration given in curve#728: 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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