Specialization at T = 388/5 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -2350796244229826784432T^8 + 40408811499609701188800T^7 - 807647185297995630241792T^6 + 1124780763822387162339456T^5 - 1304766910580579021664360T^4 + 1443539650170624433343496T^3 + 1704268062115609657765788T^2 - 1468913167837302046081776T - 1000351384601036369237532,
A6 = 39869593619137462773895754588544T^12 - 1348966735043080317092632272134400T^11 + 31027342372605406058463256507914496T^10 - 139468061144328757444897112746057728T^9 + 1081825061951776499965823580935603424T^8 - 1898481303093606040657233497704979232T^7 - 570283484013752985306584054565000912T^6 + 2509799809819326794944663142993968224T^5 + 574280708473637397501657996019459428T^4 - 2029433790678638479785535621658530032T^3 - 641250037642162230715032671759921448T^2 + 863840080098002956108405878211611888T + 384816973441734885044295380206073844.
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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