Specialization at T = -469/370 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -6045653798989791126192T^8 - 62415704538217319360448T^7 - 1599340192212345051878944T^6 + 411285604330977976052256T^5 - 987166911410498278789680T^4 + 1046627474370060703109584T^3 + 194010634771867183414656T^2 - 729479896920873105811452T - 225965831905541594247667,
A6 = 163989304706795551092980878190976T^12 + 2463417736840188795628573229020416T^11 + 99064787504796030904023011794321024T^10 + 306093533334403679180135432179319680T^9 + 1458791938240704239622260678224652160T^8 - 2067052078435764908208365147286526272T^7 + 225696680714681572698300960927997248T^6 + 1453625359670481930865233085816499472T^5 - 247522312386237949189300655828535660T^4 - 553746777745423527483394159931837640T^3 + 133678131457935919739674847770663476T^2 + 203231717596297497476228246857348516T + 40705869704413231155701476152234574.
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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