{
  "id": 53,
  "curve_key": "336:-5400",
  "ainvs": [
    "0",
    "0",
    "1",
    "-7",
    "6"
  ],
  "rank_lower_bound": 3,
  "naive_height": 17.451333479889612,
  "faltings_height": -0.5613901422939866,
  "conductor": "5077",
  "bad_primes": [
    "5077"
  ],
  "discriminant": "5077",
  "regulator": "0.41714355875838396981711954461809339674981011",
  "points": [
    [
      "1",
      "0"
    ],
    [
      "2",
      "0"
    ],
    [
      "0",
      "2"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Smallest conductor of an elliptic curve of rank 3: conductor 5077 (prime), Cremona label 5077a1 / LMFDB 5077.a1, y^2 + y = x^3 − 7x + 6. Cremona's tables are complete below conductor 500000, so 5077 is the provably minimal conductor in rank 3. Generators [1,0], [2,0], [0,2].",
  "created_at": "2026-05-28 21:07:16",
  "updated_at": "2026-07-01 23:04:07"
}