Specialization at T = 653/80 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -5295620710700377671600T^8 - 94037966474871021583680T^7 - 590731768793188987891776T^6 - 316565515830122546981184T^5 - 762681779746720476850440T^4 + 1987613918828860347667800T^3 + 1569564836467837283726676T^2 - 3214905333565214256563376T - 2212765344524109268510452,
A6 = 149936157543712438778032606320000T^12 + 4003077612324280274862537287520000T^11 + 40256463697048454693428799356032000T^10 + 181374780086403872414844938171109120T^9 + 402662249843699366956864710038784096T^8 - 758031533540911762791576885234671328T^7 - 399143032260021392125750735091011632T^6 + 2151897782383821345209559268211414304T^5 + 557784900106071266465324558195950116T^4 - 3137783098558594528537444090769421600T^3 - 420721733859426366310009677118678488T^2 + 2767709433062054442394845582008506272T + 1268413949854822572813035476740281796.
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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