Specialization at T = -29/96 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -6490299971789709696747T^8 - 122171843220159373604496T^7 - 507701052166171299717636T^6 + 1050551383991494297232448T^5 - 1535498496547466925264930T^4 + 2182465350304253473007088T^3 + 607653974805791446562364T^2 - 1786833563705739775293696T - 740288204118893840150907,
A6 = 301250623701631052997714872966886T^12 + 5692055598226519603489686839092272T^11 + 35336888180450378093651037180173676T^10 + 117205369002705497808649348735832160T^9 + 178701654202460409889459615037185530T^8 - 1878311915395808086196582818654473120T^7 + 1979838463701093911232660031750203240T^6 + 1153701456205174682023944677522475360T^5 - 1378053281785187552098745035715906070T^4 - 1354630698351600468048880643107976400T^3 + 348278788638126247479431301650393100T^2 + 854663677517493018162704474754865920T + 245812677073686954605814171513689430.
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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