{
  "id": 4584,
  "curve_key": "151423434023626520264156087078427669954175921:-1910605909216812885537822134188464775903729144515456018238618132969",
  "ainvs": [
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    "2211349431963903802705549767404432101994598275908377750849174617"
  ],
  "rank_lower_bound": 26,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 305.23607311863043,
  "faltings_height": 23.341924905210387,
  "conductor": "263542669493980362273701944576786465311279689102958423623867133463127042831994298942466417531070",
  "bad_primes": [
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    "3",
    "5",
    "11",
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    "19",
    "23",
    "41",
    "47",
    "59",
    "73",
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    "9817",
    "231634667493284287",
    "73315279431040153541",
    "1274688633367886253095517054987462043"
  ],
  "discriminant": "-103251438448619135013708103418624349100934288891270198726609406040931178740946698796726672519734789357661214436874275450880000000",
  "regulator": "261972076220345130819397420.766729406083792756321921866610388339048588932836350343097904654",
  "points": [
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      "50597067988048777442533772524163"
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      "-13619459160942709604113376188117"
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      "2816761882405392222458",
      "-125196014634594877881200897431549"
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      "781485972384986151674",
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      "-22527973036501932480569221364557"
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      "-7458097899114135446135934931837"
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      "725027369142069576284714/961",
      "481055651534937670477070183451599933/29791"
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      "1104558750773214654074",
      "8629294576971800994935764175363"
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    [
      "-1925392752930963656326",
      "33876302427778987150323848812163"
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    [
      "-1758048004863212424326",
      "48205057115199807427775473836163"
    ],
    [
      "7548163430357341287158",
      "639104360076950716860359427508511"
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    [
      "1284036151347569945174",
      "-16664682393342092949235099374337"
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  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 1634/921 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -94521237307405223348592T^8 + 194603007768925915807776T^7 + 374678018163025368194124T^6 - 569211691896707346596088T^5 + 55463370301014723924120T^4 - 1135612908646444410668928T^3 - 2702507543729482509654336T^2 + 609092474805433024526016T - 184694377125002807554992,\nA6 = 11265741534554236438342976060251776T^12 - 34833166213267258548363680994916992T^11 - 69502033189823387959197312852122064T^10 + 265587490260133017697161120524802480T^9 + 273144084685427886803017231992231060T^8 - 1114854493674664679669934784078225824T^7 - 766273999597311933358466543970856272T^6 + 2407762999977059159006184076291662816T^5 + 1357060199643920217443950358505612000T^4 - 540509467373796107556447739286515200T^3 + 808090270114106954000628418781159424T^2 - 154315127645781466989761857773289728T + 30433563297067405810172392059479424.\nIt 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.",
  "created_at": "2026-10-18 10:10:32",
  "updated_at": "2026-10-18 10:10:32"
}