Specialization at T = -153/175 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -6276238998830220029652T^8 - 147117265740737393263056T^7 - 1476608115021273186431436T^6 - 2537588378961323810084232T^5 - 2548792821173728264463880T^4 - 1085007595485857335267392T^3 + 1266527474226087852521664T^2 + 648517828968568984999104T - 394596892599474187722672,
A6 = 183805362097981758392518604760804T^12 + 5732624758080384420828430168047168T^11 + 73959871695264874512454632891659784T^10 + 444783553219225017837165953570627520T^9 + 2344794983173561552804045815952068900T^8 + 3952769116759113473247850984388751264T^7 + 1034132030293362061211853414656889168T^6 - 2105709468706045084822083295783288416T^5 - 399200243459621989020610997025954720T^4 + 954359071876325078141973753377053440T^3 - 120506571390369672930568955416602624T^2 - 234913768366312396616401364230326528T + 83823186438658476366371918607332736.
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.
apkorte ·