{
  "id": 4053,
  "curve_key": "3140613997575457:-175995333875000106896689",
  "ainvs": [
    "1",
    "0",
    "0",
    "-65429458282822",
    "203698297643610081636"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    3
  ],
  "naive_height": 107.0495841490332,
  "faltings_height": 6.5937503168063945,
  "conductor": "13047414767043566",
  "bad_primes": [
    "2",
    "7",
    "13",
    "19",
    "31",
    "37",
    "43",
    "97",
    "103"
  ],
  "discriminant": "1707938204811166123135801474391289626624",
  "regulator": "7039.893953051426596738068499939524216570435190404977",
  "points": [
    [
      "4714412",
      "-136128662"
    ],
    [
      "41229964/9",
      "8499528238/27"
    ],
    [
      "-1653460",
      "-17530940054"
    ],
    [
      "6403372",
      "6873404778"
    ],
    [
      "-1024015924/121",
      "16377281123870/1331"
    ],
    [
      "4962436",
      "-1103670286"
    ],
    [
      "-8130932/9",
      "-437081279954/27"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/3. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-10-07 22:25:04",
  "updated_at": "2026-10-07 22:25:04"
}