Specialization at T = 307/19 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -48788204994959095721152T^8 + 292967918358775673142176T^7 - 257383034328976566251548T^6 - 697546673797396881668416T^5 + 120168749817393327515900T^4 - 1757567929634520292525024T^3 - 413537200758726229861444T^2 + 1707114327506779370979968T - 562162388405818919328652,
A6 = 4093740998135849949800603694210304T^12 - 39254200079660475614530561864102528T^11 + 106574491886043297526892628627228560T^10 + 93605566178607331448553679365937280T^9 - 784525015208748993169852391016411996T^8 + 155163719535379155266150397777650688T^7 + 2578710394897183836702469318351911360T^6 - 11129400918516684422195231027746944T^5 - 2571149805127224053198426441759406936T^4 + 885351238544731577742776581975479680T^3 + 1010399979603017167929810575585795728T^2 - 806575307806361814743442724032893696T + 165741056816888627629082643287877460.
It is a 2-neighbour of the fibration given in curve#4191 (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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