Specialization at T = -318/133 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = 1840758517133685517328T^8 - 28551969868039231295840T^7 - 1772998693252999313402080T^6 - 759387847760867496814400T^5 - 598922555435041558626640T^4 - 544800986643777256848080T^3 + 926816232306216461908040T^2 + 288493294443742559437240T - 230970134041531372322875,
A6 = 325113825546664597334681997252736T^12 + 13439521326531181915894800771978880T^11 + 138327069120450496577609764257248960T^10 + 3518007078129231511599849398766400T^9 + 1769321142185421847687389290390981520T^8 + 1594947821477300217886357939071742368T^7 - 1479100347162091017597427825166729760T^6 - 1235366662137150944785202891205624960T^5 + 731032719531350653488345005675279040T^4 + 467848968404338281084037609996168720T^3 - 249593152301734103394166433543833544T^2 - 84246673758026015337923892531146920T + 42769382258496484819391456728787350.
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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