{
  "id": 3410,
  "curve_key": "6702304870777:-17351469786148145101",
  "ainvs": [
    "1",
    "0",
    "1",
    "-139631351475",
    "20082708023947730"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    3
  ],
  "naive_height": 88.6004177811934,
  "faltings_height": 4.366202364988621,
  "conductor": "2082754778",
  "bad_primes": [
    "2",
    "13",
    "31",
    "109",
    "151",
    "157"
  ],
  "discriminant": "-4165509556",
  "regulator": "5502.127405897948522788794551500421764218901272",
  "points": [
    [
      "3816224871/17689",
      "-253780129574/2352637"
    ],
    [
      "154959",
      "46468198"
    ],
    [
      "9244253935/42849",
      "-955011427910/8869743"
    ],
    [
      "311525795/1444",
      "-5834461415/54872"
    ]
  ],
  "submitter": "hdeping",
  "history": [],
  "commentary": "Found by a Mestre-Nagao sieve on the Z/3 family E_(a,b): y^2+axy+b^3*y=x^3, t = -1609/1.",
  "created_at": "2026-09-26 22:30:40",
  "updated_at": "2026-09-26 22:30:40"
}