Specialization at T = -148/49 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -37778694267449139654832T^8 - 165004421248548489849920T^7 + 23964366446631678311360T^6 + 575308331009960686683200T^5 + 644216561885971678915960T^4 + 812460692539323896913800T^3 - 3819953879838341796444940T^2 - 3397350178704392175665600T - 728947575597452632980100,
A6 = 2901058156988098667187936175477120T^12 + 21730259143975499723992766217644800T^11 + 17535187883067791568400114163932160T^10 - 192962391515084787078631234218208000T^9 - 223683722196314018130030826199045280T^8 + 1043994033704842065087271937128639200T^7 + 875242041280405478572518252943970640T^6 - 3146689238453170755654295705800631200T^5 - 1529213271890985767861180186700707580T^4 + 3040571437100170751919897956070815600T^3 + 3919924516140400157697908339646928136T^2 + 1660827326525159620863953893304037040T + 238239533579990858915246998091788900.
It is a 2-neighbour of the fibration given in curve#4187 (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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