Specialization at T = 2748/203 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -8601190111439927121627T^8 + 70553802194275661608968T^7 - 40117514965744884873804T^6 - 394125757357369375667736T^5 - 727539205447352323463130T^4 - 3371639403550126915091304T^3 - 358500560703347306973924T^2 + 5575527756032095197563112T - 2574982297007819942866587,
A6 = 311073935845060124132541860022390T^12 - 4299424530738788428378210804267800T^11 + 17883941445167312163435648485037300T^10 + 19652059401694206221665695004579800T^9 - 317465301013995782557083261357635310T^8 + 112305603376549774936723074091082640T^7 + 2598376408341179206723494257772920880T^6 + 911887687830002593185098844364676160T^5 - 4509956533653094383564183143089914510T^4 + 1581320920924061257174062701329500840T^3 + 3668404075692271898587012925610059196T^2 - 4676936909330964399995425467736251576T + 1568898839279682527117596188509969334.
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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