{
  "id": 3759,
  "curve_key": "3544541152:-211027976347096",
  "ainvs": [
    "0",
    "1",
    "1",
    "-73844607",
    "244220728125"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "naive_height": 65.96602365987631,
  "faltings_height": 2.6275012393840815,
  "conductor": "14526811",
  "bad_primes": [
    "13",
    "19",
    "103",
    "571"
  ],
  "discriminant": "-14526811",
  "regulator": "482.60662064579865213684679244799978049325979",
  "points": [
    [
      "2693",
      "254744"
    ],
    [
      "5969",
      "127071"
    ],
    [
      "288140079/58081",
      "-6994932/13997521"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Found by an exhaustive discriminant sweep of the integral Tate X_1(3) family y^2 + a*x*y + b*y = x^3, for which Delta = b^3*(a^3 - 27*b), below the previous rank-3 discriminant threshold. Parameters a=244, b=-1 give Delta=-14526811. PARI/GP 2.17.4 gives rank bounds [3,3] and torsion invariants [3]; the three supplied rational points lie on the global minimal model and are independent.",
  "created_at": "2026-10-01 17:49:12",
  "updated_at": "2026-10-01 17:49:12"
}