{
  "id": 6031,
  "curve_key": "2981133778752:-5147213685083054136",
  "ainvs": [
    "0",
    "0",
    "1",
    "-62106953724",
    "5957423246623905"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 86.16997442027025,
  "faltings_height": 4.177572808541239,
  "conductor": "2268747171",
  "bad_primes": [
    "3",
    "277",
    "439",
    "691"
  ],
  "discriminant": "-2268747171",
  "regulator": "3787.1543868179440596537896313012273288939376",
  "points": [
    [
      "6775306623/47089",
      "-5085828/10218313"
    ],
    [
      "74638649934001/518746176",
      "1587773037498263/11814962904576"
    ],
    [
      "2263702008073155/15732935761",
      "-986656283005176/1973397865437991"
    ]
  ],
  "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=1314, b=-1 in y^2+a*x*y+b*y=x^3 gives y^2+1314*x*y-y=x^3, with discriminant -2268747171. 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 14:14:29",
  "updated_at": "2026-10-28 14:14:29"
}