Specialization at T = -4927/4396 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -234114040453021356506112T^8 - 272002889947768518314880T^7 + 686028086039421713758320T^6 + 1142195364874563315587280T^5 + 627637229082985727538360T^4 - 984449918457333810927360T^3 - 2633542817168016219118320T^2 - 1006973197204579283167560T - 114715927313180034201675,
A6 = 48308501179046578125484559991177216T^12 + 57069826702680132557515086694133760T^11 - 311131671782769127044180046463351040T^10 - 240521895686500160053739383108517760T^9 + 1147866319247799475598436207881897040T^8 + 683399028950475828317237644205746752T^7 - 2372093631572614744214600133762992400T^6 - 1765634230326260432804074074782197200T^5 + 1564909970672513896400523764894111640T^4 + 1894740665595018649008096627125850240T^3 + 882898465151004944410908107862516576T^2 + 191456284444900580427321522994041240T + 15250200281398537130338745700198150.
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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