Specialization at T = -1/2 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -51049289999914003955547T^8 - 530235497365547560296156T^7 - 1334884185331356871311696T^6 + 296356690966601689934112T^5 - 953952652223826315944400T^4 + 1047754795078929750243552T^3 + 682302168670760680583648T^2 - 366523380774730949131328T - 202247154940524926594992,
A6 = 3044477113558101150415568243130870T^12 + 47916509824848437926710847832831508T^11 + 305385110180964852636417452183552148T^10 + 946395756942760565659602913027215240T^9 + 758039466954512559172972729736599956T^8 - 2347628404098854859298591084323198768T^7 - 233574834077417409656982537875304960T^6 + 1478394126214621260825428576579913984T^5 + 245358536538278262563954912437168896T^4 - 564843727808435860192153910652566400T^3 - 138927685606375319261165262679233920T^2 + 99890538814857739577414321265656576T + 35404124129085042130410014629000576.
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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