Specialization at T = -257/517 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -113946597679617331526187T^8 - 628704898397157619416528T^7 - 910139814353468861642484T^6 + 13879376823678260295456T^5 - 533762798296920925528530T^4 + 1639003787601085356814224T^3 + 806892413125232101174956T^2 - 592355532948433669282752T - 295458143973808062849867,
A6 = 15882493844523546552540807840095910T^12 + 145809795943145321517489625166050800T^11 + 489200782557326126999832807296770620T^10 + 474439873253302462549441686771960000T^9 - 939321256931213164482716468158448790T^8 - 1775504390224299025107326496664527360T^7 + 1396226578858524162480471413923945800T^6 + 1631143206019716771050709031938957120T^5 - 432541045559235732878122118765459190T^4 - 878384718510400823408137143448720560T^3 - 116676491482650081744926274060252324T^2 + 185829851435689714140802850197329216T + 61035568685910358648726719363207174.
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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