Specialization at T = 433/670 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -5359397556934326557952T^8 - 135465106160634648571008T^7 - 1009560857120332086707244T^6 + 302645697651446768292456T^5 + 267102270709279813507320T^4 - 18710244598364193145536T^3 + 1090445903163236801932416T^2 - 91760564814653904426432T - 567824854400092808778672,
A6 = 156065240689863717949223596360704T^12 + 4827291258544591401284174444461824T^11 + 48077643204571887106158625640791056T^10 + 215456560411136671924188808659259680T^9 + 998209464630408701484689228105999700T^8 - 909644941490611250119006829109042720T^7 - 2569542697812503924009268807282804720T^6 + 1241192156761670225595583604913427680T^5 + 2544459298635871164419215332497359200T^4 - 725030770745235523201629773993683200T^3 - 1216067410812944483775200857080372480T^2 + 159116305290413916148713260094977280T + 238920668104630371120386669007676800.
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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