Specialization at T = 10/3 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -52648197173377472411667T^8 - 502136288453868619765932T^7 - 1375723089516896204761224T^6 - 113586999512798824277616T^5 + 115484330308006964556720T^4 + 1146633583580186797214496T^3 + 875307711060207742486176T^2 - 552420246310353167485248T - 379684178449627628010672,
A6 = 4604058775563334978457275228090926T^12 + 65897015586211952847350301356878644T^11 + 353596781702159377755551694850071564T^10 + 792468362119369014579444750140997960T^9 + 225448975378970803493231159228247540T^8 - 2087772451361914308664322072224378224T^7 - 550444434966430640467599977153927136T^6 + 2077986353393758716550697478306369984T^5 + 497054571856074095600647080235134720T^4 - 1050047839109210694723463620193948800T^3 - 326801521813959825897823057885147776T^2 + 226384397181047822018105284978542336T + 93697525934370302137180629038948736.
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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