{
  "id": 1619,
  "curve_key": "312420879246864119449:-5402783079266479914534768642493",
  "ainvs": [
    "1",
    "0",
    "1",
    "-6508768317643002489",
    "6253221156016028467204250536"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    6,
    2
  ],
  "naive_height": 141.57264877380646,
  "faltings_height": 9.69741947589256,
  "conductor": "52197440565270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "29",
    "41",
    "113",
    "761"
  ],
  "discriminant": "754825858558426405448779333085893008126075033109891016100",
  "regulator": "496.2304760947666150126948371975978594408306990",
  "points": [
    [
      "3271310255",
      "141309551922432"
    ],
    [
      "1710669404",
      "11177509921548"
    ],
    [
      "515394164498",
      "370001625555146478"
    ],
    [
      "1458050815697/64",
      "1749981517299291261/512"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/6+Z/2. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-25 01:42:12",
  "updated_at": "2026-09-25 01:42:12"
}