{
  "id": 4983,
  "curve_key": "48453396530311636879233600:-335892688827167333377673465189299776000",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1009445761048159101650700",
    "388764686142554784001936881006134000"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 177.42793401468455,
  "faltings_height": 12.61342927007384,
  "conductor": "20238386706299310289552929600",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "37",
    "53",
    "79",
    "151",
    "443",
    "467",
    "1877",
    "1951",
    "11329"
  ],
  "discriminant": "539162885155027115777493333246787081864855310068919051247276840960000000",
  "regulator": "378536112.29822856088822205981677401486085084735967823798",
  "points": [
    [
      "-1152867950114",
      "142268615798523984"
    ],
    [
      "393737619949",
      "228798574265141757"
    ],
    [
      "667120273630",
      "110654737856506800"
    ],
    [
      "1193694589480",
      "940583993162883300"
    ],
    [
      "9660194212180",
      "29868384435036877800"
    ],
    [
      "-6620677546154930/6889",
      "392518041177057828051600/571787"
    ],
    [
      "-636391368432770/1681",
      "58345644581485452298800/68921"
    ],
    [
      "1910033547214/9",
      "11584627644937675888/27"
    ],
    [
      "1629146799219247630/3200521",
      "472957350474986870947405200/5725732069"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Michael Rubinstein's elliptic-curves-by-rank repository, families/family_Z4.part2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Nine rational points checked exactly; PARI/GP returned rank bounds [9,9]. Rational torsion C4. Source-attributed existing curve.",
  "created_at": "2026-10-21 01:08:57",
  "updated_at": "2026-10-21 01:08:57"
}