Specialization at T = 5411/3949 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -58701756188828782740672T^8 - 421589935203760423753344T^7 - 677464368389618755113936T^6 + 669015607734413855170992T^5 + 1311645217705022688331320T^4 + 1050713078894545198928832T^3 - 1636359720229735222434336T^2 - 2517746756775352549692984T - 810344655390742277047947,
A6 = 5480627817022307258018449212308736T^12 + 59387395680501866438327388746270208T^11 + 202192728222021747784840349845289856T^10 + 81426836279267976104124948661760640T^9 - 731444121000417496333010776856855280T^8 - 504969396495943282941884145271012800T^7 + 1906585932510725663650827845073118320T^6 + 512612498829370479665585111044169040T^5 - 2456755728368285626110680543972723880T^4 - 642737286070578650255592249597744000T^3 + 1935352237260464424985879727209027440T^2 + 1451023268234470568001166626460852200T + 303174450039421684871841546202620870.
It is a 2-neighbour of another fibration built here: 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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