Specialization at T = 3/4 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -78933294009407830037787T^8 + 664351884165635092112904T^7 - 2021985732877889552885376T^6 + 548914813539097302606528T^5 + 640067948619176548996920T^4 - 1474849384729522256976912T^3 + 590464289390067586470384T^2 + 586034868174794137776384T - 300031800937869261707712,
A6 = 8561696935567950178044488886746934T^12 - 107576211314584682375352315962746392T^11 + 546348427718307812695067413402466064T^10 - 1166581522203545622660674205159843840T^9 + 773302754513408948238245171376141720T^8 + 1872425742961196136859874329988857104T^7 - 1253513330397887853768088296036034512T^6 - 1224384265855733627043677184733740096T^5 + 513489745068218712536403992172247440T^4 + 606394277930394193521826714846596480T^3 - 152435778857543725795710547166980224T^2 - 181401199060234447536055851013959168T + 63554942967600090043999344449500416.
It is a 2-neighbour of another fibration built here (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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