{
  "id": 54,
  "curve_key": "3801:-232605",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-79",
    "289"
  ],
  "rank_lower_bound": 4,
  "naive_height": 24.729058406967745,
  "faltings_height": -0.08697563887120269,
  "conductor": "234446",
  "bad_primes": [
    "2",
    "117223"
  ],
  "discriminant": "468892",
  "regulator": "1.504344888275283974095271252282834672518585514",
  "points": [
    [
      "6",
      "-1"
    ],
    [
      "4",
      "3"
    ],
    [
      "5",
      "-2"
    ],
    [
      "8",
      "7"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Smallest conductor of an elliptic curve of rank 4: conductor 234446 = 2·117223, Cremona label 234446a1 / LMFDB 234446.a1, y^2 + x·y = x^3 − x^2 − 79x + 289. By completeness of Cremona's tables below conductor 500000, this is the provably minimal conductor in rank 4. Generators [6,−1], [4,3], [5,−2], [8,7].",
  "created_at": "2026-05-28 21:07:17",
  "updated_at": "2026-07-01 23:03:09"
}