Specialization at T = 13/15 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -12534891445024511472T^8 + 78582946111770655584T^7 + 7309714285353743792064T^6 - 19926705130047311795712T^5 - 1581992160157740826540080T^4 - 21656860033375553017441392T^3 - 202996255697903740935519336T^2 + 178453288354749583292951064T - 417819161395360164489662107,
A6 = 17317363417405211174636142720T^12 - 210396669596964946038298988160T^11 - 14361293747299826509324376137920T^10 + 234213338250246103165559236334400T^9 + 4592862633125351988053413995183120T^8 - 107548397787843527128824559544935200T^7 - 702154954133939094763560787985051520T^6 + 29466052944788501707392754934785197120T^5 + 255347880900757963651505245178114673120T^4 - 1780579839791453417816567234531995600T^3 + 2459557153650501225624269205923573478216T^2 - 2269524913223376034392201865605330615368T + 3342509745342723924186855161219248634806.
It is a 2-neighbour of the fibration given in curve#4191 (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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