Specialization at T = 3/1 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -208105972076488790307052T^8 - 439527670947297931328940T^7 + 343660503631112086072245T^6 + 613353394224090550622880T^5 - 231043158672102674134740T^4 + 1208678840215888066067520T^3 - 559641271407448823804880T^2 - 714118514352617716439040T - 146036624395308969816000,
A6 = 48948478213224443067242844627078004T^12 + 208793951588984308688304222760788820T^11 + 53897690802776318918669214864929865T^10 - 939263184673604027480558480888431240T^9 - 926917487525195732269342791952526655T^8 + 1746605331713416582793524688175626496T^7 + 2007083092390584405960569676783621120T^6 - 1692632433459306707439291235219046400T^5 - 1287348467089494424054800792979985760T^4 + 176901482519389361500233479886873600T^3 + 435942394999692519911189932156974336T^2 + 166662302037719363510662729228216320T + 21432169750567610095158106104249600.
It is a 2-neighbour of the fibration given in curve#4187 (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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