Specialization at T = 3904/4935 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -11696112421636110725232T^8 - 225953091010175473234080T^7 - 1285862935447903797580320T^6 - 1129158151626029959937952T^5 - 1592088393814170815994480T^4 - 37631263114247380337808T^3 + 1695532195366906279824008T^2 + 289018889748535735084344T - 624976459672410496278747,
A6 = 449725080902042019431313876378240T^12 + 11412860638353264300064607972424576T^11 + 108724211594005774585272702173979840T^10 + 552699339212501471676010717898982720T^9 + 1706301350149364859650702774642594064T^8 + 698629245250434441649386767885626848T^7 - 1435130050396849573556196386817943392T^6 - 607341322268570723710732507501947360T^5 + 1272148652815891722874496655477939744T^4 + 339936587466097075261357997400067920T^3 - 735579972865799521796462939416343048T^2 - 132384785109517617529019092091956392T + 190126813773008796183739475605546614.
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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