Specialization at T = 1/5 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where
A4 = -129077164062048809835900T^8 + 378319182388641891290880T^7 + 136088129918041916509980T^6 - 755961738076060064377560T^5 + 619450622573441931032760T^4 - 1170861959203596215660160T^3 - 1734751811488996657912320T^2 + 1314050376486783211611840T - 219065110811691252584112,
A6 = 18245050345346515787515057919752500T^12 - 83505322013254826025359146692690000T^11 - 2407103439528010819936132599838344T^10 + 465220783429849849086641780587731600T^9 - 185239629309258027189063745343474940T^8 - 1503733795718269687786747306505656800T^7 + 626403979186422524394828379594167600T^6 + 2519798602559624814688441138399867488T^5 - 832465009702733039267308016691100320T^4 - 905573011434584900869203229631278080T^3 + 930446348033589270658482617988215040T^2 - 337397396218794978267255003741415680T + 42647307174629128234916120026233216.
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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