{
  "id": 1264,
  "curve_key": "771916746638573527207609:-678186331321506511704789277791621037",
  "ainvs": [
    "1",
    "0",
    "1",
    "-16081598888303615150159",
    "784937883472625736787999325811122"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    6
  ],
  "naive_height": 165.00949096782816,
  "faltings_height": 11.39094414627422,
  "conductor": "21562908872242620554490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "23",
    "43",
    "47",
    "59",
    "199",
    "4253",
    "200171"
  ],
  "discriminant": "8166114877639432463036856964198124648037817276784265373786056720",
  "regulator": "633795.1518816153924383957740665848617752755035709031",
  "points": [
    [
      "1851340334574/25",
      "47227468910185208/125"
    ],
    [
      "2943160734136/9",
      "4715148081806169970/27"
    ],
    [
      "72919982379",
      "-84510781248620"
    ],
    [
      "40024311963523/81",
      "245582589116776649336/729"
    ],
    [
      "25947143135167855/239121",
      "2083766186244555794247232/116930169"
    ],
    [
      "169560539754689713/576",
      "-69821175766117362705718267/13824"
    ],
    [
      "34578122648935570824/3575881",
      "-203312941894506192957530381630/6761990971"
    ]
  ],
  "submitter": "hdeping",
  "history": [],
  "commentary": "Found by a Mestre-Nagao sieve over the Tate normal form family y^2+txy+(t+2)y=x^3 with torsion Z/6Z, at t=-952001/50439.",
  "created_at": "2026-09-24 16:47:55",
  "updated_at": "2026-09-24 16:47:55"
}