Specialization at T = 0/1 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -7760309087359314183600T^8 + 119026997715519499556160T^7 - 1153373924390107974174144T^6 + 2487025529977453776585216T^5 - 3661714748108170932991560T^4 + 1974920503429370676448440T^3 + 1022466571703719091443964T^2 + 405620581566251073119344T - 1286300189709170452777792,
A6 = 264858137926126918747215127920000T^12 - 6183711970751924651607354681696000T^11 + 81178268015262088437641813152396800T^10 - 478686331323910127099177745304273920T^9 + 2005108572441196128294357056113536864T^8 - 3279557226608882175286227464412177888T^7 + 1865313942900757552134099206544410352T^6 - 915373920036612203329630698180943776T^5 + 2248150939946977357222177775373137844T^4 - 1203506060647437664686363673157004240T^3 - 593281745909986606769035134794080016T^2 - 270618994174348662640690696819440256T + 561058323515548891363915496659302400.
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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