Specialization at T = 50/61 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -10669947921935414766592T^8 + 11909462495223346810112T^7 + 29290850738695015599056T^6 + 749826724411797003953776T^5 - 2800296645908250177432680T^4 + 5291011042236720751525024T^3 - 9053743075112346775820704T^2 - 1373686135035664689321352T - 153062929487822447776267,
A6 = 424084459520579325699737587892224T^12 - 702971076900016054991835746922496T^11 - 1428460164091780099364248773693184T^10 - 45531551300070380060674898437602560T^9 + 178145138683306119166957105019549520T^8 - 224307849011465835658368095576866752T^7 + 1890363249575504635685922631864051728T^6 - 8402714629932209203714457518206796848T^5 + 10932033646871752694840038266436614840T^4 - 1045636958253350245306227479236779680T^3 + 3911537622199302231442442603656239344T^2 + 397823992391227625022128206594583384T + 16543056563137220502197778370669126.
It is a 2-neighbour of the fibration given in curve#4205 (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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