Specialization at T = 602/177 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -527341140801402202800T^8 + 28147421355562296077760T^7 - 459551759375096200061280T^6 + 302351267241048825914400T^5 - 781968800173412856857040T^4 + 675358902068135754436560T^3 + 3773048587407798267814920T^2 - 1117382211836832683478780T - 4020150123856377627416667,
A6 = 17121088738199440047220335446400T^12 - 754628062801204312746404692573440T^11 + 9968619820015289906033818763984256T^10 - 51608554478585574595758963618583680T^9 + 526057596644710242384434966047683840T^8 - 378806199877031919118656099183432000T^7 - 1773421996954369325651890262968908960T^6 + 1196920464887427116679365802787354320T^5 + 3649727616935479672514463019748893140T^4 - 2090084281847145605737007981579064600T^3 - 4861031233659870921990346669248956340T^2 + 1412045054473207996392438591189858420T + 3148792632832054337655276106728582390.
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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