Specialization at T = -715/1029 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -9801785533668367408277499T^8 - 121843241966486333706286824T^7 - 383434732762042957835672232T^6 - 85754468638713501529031952T^5 - 584201627367901316547607440T^4 + 1235140044591109335942134016T^3 + 994771523582906627448194816T^2 - 550790635100880788122728032T - 647714191600162651688347312,
A6 = 12142329458953725303990225302566830294T^12 + 247791101750863056653001398463488667192T^11 + 1886090538602583189200926091842195641480T^10 + 5912076790668428510577901681319655809040T^9 + 1282952245208814516295621371483268940160T^8 - 25791045529140834460411754210526102555072T^7 + 619130399100809058015628676691838434624T^6 + 31601519751505535243254509940106610677280T^5 + 10405299225003196422075679041028274690640T^4 - 27172444692997266799042742904489658895040T^3 - 13432438015701644454859263568215615214016T^2 + 8212424024664720375926323815936672405632T + 6370397708074310285430666560056789129600.
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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