Specialization at T = -7/6 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -25587393138499560595632T^8 + 221437887745294106450208T^7 - 409046233823443618010496T^6 - 337430027367784463054400T^5 + 385077858934643123416560T^4 - 2022438225360352683878928T^3 - 482435290242461337479784T^2 + 2239541715059421343407000T - 777998140618398505576875,
A6 = 1764219405629347358705661608694144T^12 - 25198292331980051240841044609464704T^11 + 115199016267831836970321760720675392T^10 - 75546422101413012064473686732126400T^9 - 692303544256347632957776668963449136T^8 + 753807318552830839318219503747529632T^7 + 2470157439450075720627076783725847488T^6 - 866460061617253657076985369541871616T^5 - 2899680871912044976732713869657546496T^4 + 1311833024050784553300452787956054160T^3 + 1368776544240715088543951830367560200T^2 - 1167871608295534448326902047444325000T + 245730438412887456689875458237843750.
It is a 2-neighbour of the fibration given in curve#4647: 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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