{
  "id": 6158,
  "curve_key": "1221133812079821207335741376:-42739964311784917863129645544543256670720",
  "ainvs": [
    "0",
    "0",
    "0",
    "-25440287751662941819494612",
    "49467551286788099378622274935813954480"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 187.11190608330213,
  "faltings_height": 13.383185091443192,
  "conductor": "377506140113070570556100346470719720372070066562227191140440125824",
  "bad_primes": [
    "2",
    "3",
    "7",
    "23",
    "31",
    "3952129569559",
    "4005027920188051305089",
    "4148081192219748386154707"
  ],
  "discriminant": "-3350199755263382102518069658025348217700239250723718722227913372588738961408",
  "regulator": "8022392675622538513.65049902603565171898316761711512031445887931451574942567594",
  "points": [
    [
      "2815060712022",
      "399666645897452892"
    ],
    [
      "3008975172258",
      "-401761651154070564"
    ],
    [
      "2802428158578",
      "-426769679436129036"
    ],
    [
      "1551693559240",
      "3705147137060093060"
    ],
    [
      "2310660289986",
      "1738002518707996548"
    ],
    [
      "528577722966",
      "6013988990349671772"
    ],
    [
      "2932802587749",
      "286732288698262029"
    ],
    [
      "6423466687644",
      "12291903150065803656"
    ],
    [
      "2676965736213",
      "740471985901068939"
    ],
    [
      "18571161735573",
      "-77343283979949166389"
    ],
    [
      "2927942032108",
      "-283998843440765936"
    ],
    [
      "2930884413414",
      "285569817981356916"
    ],
    [
      "3994563458598",
      "-3403543444939069236"
    ],
    [
      "14532746763366",
      "52431641164100976372"
    ],
    [
      "-3095560744410",
      "9927552967799552820"
    ],
    [
      "3596986338973",
      "2120874985392622361"
    ],
    [
      "2695806109128",
      "-690572334648824964"
    ],
    [
      "2540675575878",
      "-1110034534116285036"
    ],
    [
      "-2520210438126",
      "9878026756080088404"
    ],
    [
      "12862691343858",
      "-43015743604145048436"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -1/3 of a rank-17 fibration of X1008 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -2350252713284250372T^8 - 50405464050571118556T^7 - 952448555730502901313T^6 - 695049490520215525224T^5 - 2931749924460790132683T^4 - 2386411337210880522384T^3 + 2409436881372804430248T^2 + 4544024515422355802304T - 2684309556378273707952,\nA6 = 1416965056476304965893460864T^12 + 45023054173800546171881279808T^11 + 917608982150765091196202404680T^10 + 4283108867178449968605589545480T^9 + 53149163760305922465025229930778T^8 + 64588783908002903981500312561392T^7 - 30251100417436562854623526202130T^6 - 127076856645436090494117187739472T^5 + 56548211197412673092440132446600T^4 + 156704525825325938035598980257408T^3 - 11739117611564936890190411272416T^2 - 136493880790478548113078471588096T + 53534237645294085780370164274560.\nIt is a 2-neighbour of the fibration given in curve#3589: 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": "2026-10-29 19:23:41",
  "updated_at": "2026-10-29 19:23:41"
}