{
  "id": 6383,
  "curve_key": "4888146459618703276547722047361:-10809094179864547209313112191194618928433528641",
  "ainvs": [
    "1",
    "0",
    "0",
    "-101836384575389651594744209320",
    "12510525671139513746635905975856139012558400"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 211.99343403645017,
  "faltings_height": 15.378270867087096,
  "conductor": "267933495334122942860610918833471852370",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "29",
    "31",
    "59",
    "67",
    "71",
    "543871",
    "1169473",
    "920442349"
  ],
  "discriminant": "-22722062486837669282133324357699987623337176872464040230881555609102226454216704000000",
  "regulator": "311996546.349227689753927255732029634265039006611554394083721",
  "points": [
    [
      "-197905534774080",
      "4991314831998510048600"
    ],
    [
      "185210005353240",
      "51187058424127539480"
    ],
    [
      "184984155218730",
      "49054737516527065890"
    ],
    [
      "6940361502283440",
      "577592716080243047643480"
    ],
    [
      "400896883810290",
      "6009667566361600304730"
    ],
    [
      "185023231928220",
      "-49389432498151330200"
    ],
    [
      "192071537178960",
      "-190937606173232919720"
    ],
    [
      "200324619565392",
      "-386274978884360402088"
    ],
    [
      "-368454071060208",
      "108720353923369918296"
    ],
    [
      "475615311704400",
      "-8465488158680722455720"
    ],
    [
      "106308398308980",
      "1698794961469295263140"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Z/3 K3 family y^2+(7t^2+309)xy-91(t^2-1)(t^2-25)(t^2-121)y=x^3, parameter t=1019/751. Family construction from the Layr Labs Elliptic Rank Challenge public repository, submission/board/3-r12-z3k3.ec (commit c8f82607a219df846ab80dd9e14ee09a2904d709). t selected by Mestre-Nagao sieve ordering; 11 points from specializing the family sections at t; PARI/GP 2.19 ellrank bounds [11,11]; torsion Z/3Z (elltors).",
  "created_at": "2026-11-02 00:42:57",
  "updated_at": "2026-11-02 00:42:57"
}