Specialization at T = 2/13 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -2241070746096641026608T^8 - 48890065197872193202368T^7 - 1242865024659722240399412T^6 - 129721360166822665555416T^5 - 1095502516682193218704680T^4 + 1203400967658358227986304T^3 + 1102484040584899813957568T^2 - 464205369490492311699008T - 340636802726403331139248,
A6 = 27904034754823698959642925455232T^12 + 2151919369557120564884658183913728T^11 + 58187531523799496672026563340878192T^10 + 172569984133100265846070068117224880T^9 + 1578209289982661012818716755624428596T^8 - 1284180339848885667921774017393210016T^7 - 1252435512115119963585561517641849552T^6 + 1259494814644547973636042498844029024T^5 + 728092080921839349171124150493358816T^4 - 708127293957126802183009949286197760T^3 - 331295715191254779558572993006363648T^2 + 156934618497934840781513210088796928T + 76614851639845112330141048005286272.
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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