Specialization at T = -3364/729 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -34563528913036557884400T^8 - 363066894139066649206560T^7 - 1253243958943048847118720T^6 + 1217803890141503318620800T^5 - 1229632829129776891166640T^4 + 889782194202589151280720T^3 + 747172710296992900801080T^2 - 433583331227756476888680T - 198981396396273976948827,
A6 = 2529174685018796943057183053750400T^12 + 38255811556046455632742522418874240T^11 + 209255178696584738819667007675000896T^10 + 459298877624289867341928240423086400T^9 + 710742840439999694736111158271090960T^8 - 2594464885975235791000216537446763680T^7 + 507169769440286090575053053081870400T^6 + 1519561014747819598698469788704128704T^5 - 146641249872692903802186384657680160T^4 - 569600267540526989066094026512214160T^3 - 74471423161824441814957627679250840T^2 + 111793067512606356283231367322794040T + 33201984796393433668897397905886454.
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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