{
  "id": 6042,
  "curve_key": "54875861920:-12854998549372888",
  "ainvs": [
    "0",
    "1",
    "1",
    "-1143247123",
    "14878089460881"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 74.18501824556634,
  "faltings_height": 3.2537062464302853,
  "conductor": "113379877",
  "bad_primes": [
    "13",
    "37",
    "73",
    "3229"
  ],
  "discriminant": "113379877",
  "regulator": "3067.8973054151978473792990998433653067253612",
  "points": [
    [
      "6326533/324",
      "7531867/5832"
    ],
    [
      "57750920289/2958400",
      "-2543892687/5088448000"
    ],
    [
      "3783713362759/47155689",
      "6790531621240491452/323818116363"
    ]
  ],
  "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=484, b=1 in y^2+a*x*y+b*y=x^3 gives y^2+484*x*y+y=x^3, with discriminant 113379877. 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 16:04:05",
  "updated_at": "2026-10-28 16:04:05"
}