Specialization at T = -336/139 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -24031029665327797232767T^8 + 179305869982048445443572T^7 - 15434043446921367581904T^6 - 1359491595553384291321920T^5 - 1251177099291190680208560T^4 - 793870677479698730348832T^3 - 465983991977317682237856T^2 + 1581044404633777347981120T - 513268853367954448263600,
A6 = 1464980610683190207683635064387170T^12 - 15226098350974251104399011548495212T^11 + 31182187814980858871948850733079604T^10 + 94882057085868263070543071690124440T^9 - 382383456053978226203046668114059644T^8 + 119987179832555651967492958730573328T^7 + 2833926355389365701285515892492966272T^6 + 1391513510216999650767496184555750016T^5 - 3206877893714253625843008218509021824T^4 - 325665422393502655104433213009299840T^3 + 1960986866227523419821124223062684800T^2 - 999490438443489710935366277087328000T + 167924010299517718017234405479280000.
It is a 2-neighbour of the fibration given in curve#4647: 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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