Specialization at T = 135/188 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -951794051889111932592T^8 + 44931125401781237315136T^7 - 935996917001646313472256T^6 + 350884544094515993044032T^5 - 1398456319949084806406280T^4 + 1757156899789831824711432T^3 + 1161615213018494249920164T^2 - 1209850628288081766896304T - 608061871140582830645232,
A6 = 16573004223094294578838161979776T^12 - 853911819873454385971944861242112T^11 + 10730626760581365984133349196446976T^10 + 28681501792522102389650863794343680T^9 + 1144251410928840595115561345197638240T^8 - 1598280314283758871148427065729397664T^7 - 426571032276915684981278470103405232T^6 + 1752000471251825933878865739300711456T^5 + 357646791216195149324748670252742580T^4 - 1462595841433547195589341024424494400T^3 - 249356805352454598151173826415660496T^2 + 545782915696199470675908824491330752T + 182530075488483105810112141784098944.
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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