{
  "id": 6029,
  "curve_key": "54875885152:-12855006712725976",
  "ainvs": [
    "0",
    "1",
    "1",
    "-1143247607",
    "14878098909045"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 74.18501951563269,
  "faltings_height": 3.2537063451357082,
  "conductor": "113379931",
  "bad_primes": [
    "7",
    "79",
    "421",
    "487"
  ],
  "discriminant": "-113379931",
  "regulator": "791.70202612973507387684938898250492309596529",
  "points": [
    [
      "9448165/484",
      "-5323/10648"
    ],
    [
      "193096909/9801",
      "42508185832/970299"
    ],
    [
      "33704884069/1726596",
      "-1129806451/2268747144"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained in a bounded discriminant-first search of the integral Tate X_1(3) family, following the method described by jesper-petersen on curve #3759. The source model is y^2 + 484*x*y - y = x^3, with discriminant -113379931.\r\n\r\nCandidates were selected using finite-field scores, then checked on their global minimal models with PARI/GP 2.17.4. For this curve PARI returned rank bounds [3,3] and torsion Z/3Z; the three listed points were checked exactly. This applies the cited search method, \r\n\r\nModel order [a1,a2,a3,a4,a6]; y²+y=x³+x²−1143247607x+14878098909045.",
  "created_at": "2026-10-28 13:52:55",
  "updated_at": "2026-10-28 13:52:55"
}