{
  "id": 6036,
  "curve_key": "1121144238585:-1187113473653011533",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-23357171637",
    "1373979767132043"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 83.23611276392612,
  "faltings_height": 3.9504045826326957,
  "conductor": "13451202",
  "bad_primes": [
    "2",
    "3",
    "19",
    "37",
    "1063"
  ],
  "discriminant": "1089547362",
  "regulator": "1233.0461239656283223047499591223251197247764",
  "points": [
    [
      "90897",
      "1329981"
    ],
    [
      "132398263/1521",
      "33659306725/59319"
    ],
    [
      "255605291727/2896804",
      "-217520098151619/4930360408"
    ]
  ],
  "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=1029, b=1 in y^2+a*x*y+b*y=x^3 gives y^2+1029*x*y+y=x^3, with discriminant 1089547362. 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 15:32:21",
  "updated_at": "2026-10-28 15:32:21"
}