Specialization at T = 409/34 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -96196961581357063033152T^8 - 399556103168445237840384T^7 + 121419290054525411589264T^6 + 1430959091691248074015632T^5 + 100688238281333139439320T^4 + 387367434659202151100832T^3 - 1953294802285379458973616T^2 - 733254399190976661626184T - 79743145896962463440187,
A6 = 11484504086394253195526049377853696T^12 + 72121229539722792963703791386638848T^11 + 54055657239595166572471510008621696T^10 - 398904635104645281362553198961699200T^9 - 498516576461076920592919777700932080T^8 + 1133982302557837972386711623027647680T^7 + 1070918296969515869033113344560286480T^6 - 2589863488770145152071246194277744400T^5 + 73956315674627679114868875249120120T^4 + 1069188646911222614852645794843754400T^3 + 580961502887065292988342169113394080T^2 + 118245525237113913102523416049897560T + 8723796687794086545932578364805270.
It is a 2-neighbour of the fibration given in curve#4191 (itself a 2-neighbour of the fibration 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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