{
  "id": 6039,
  "curve_key": "74818088737:-20464913560807729",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1558710182",
    "23686112654716"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 75.11497656217774,
  "faltings_height": 3.3437787647686816,
  "conductor": "286111226",
  "bad_primes": [
    "2",
    "229",
    "439",
    "1423"
  ],
  "discriminant": "1144444904",
  "regulator": "1101.9887070898924549194395209914089289268092",
  "points": [
    [
      "17870493/784",
      "-250186889/21952"
    ],
    [
      "33759936998/1481089",
      "-20542920403406/1802485313"
    ],
    [
      "99471173474/4363921",
      "-103883922694924/9116230969"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained in my own bounded discriminant-first search of the integral Tate X_1(3) family, following the method described by jesper-petersen on curve #3759. The specialization a=523, b=2 in y^2+a*x*y+b*y=x^3 gives y^2+523*x*y+2*y=x^3, with discriminant 1144444904. The displayed equation is its global minimal model. All three listed rational points were checked exactly and returned as an independent set, with rank bounds [3,3]. The rational torsion subgroup is Z/3Z.",
  "created_at": "2026-10-28 15:47:12",
  "updated_at": "2026-10-28 15:47:12"
}