{
  "id": 4977,
  "curve_key": "-1528521423126169559744:72899855456394911877004596475904",
  "ainvs": [
    "0",
    "1",
    "0",
    "31844196315128532495",
    "-84374832693546045530379142497"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 146.73327889213704,
  "faltings_height": 10.334915187209097,
  "conductor": "130610267722497718589280",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "29",
    "181",
    "293",
    "677",
    "1021",
    "195541"
  ],
  "discriminant": "-5142125205514529694553834533603834181870468816339928701440000",
  "regulator": "531889666.770741359406843389160628118066589373994782708",
  "points": [
    [
      "4389533721",
      "374144229149460"
    ],
    [
      "3634839259701",
      "6929921870246067000"
    ],
    [
      "25366937473/9",
      "4499430081017300/27"
    ],
    [
      "779547416169/49",
      "723465534011914980/343"
    ],
    [
      "12805876313641/576",
      "47108526270746227595/13824"
    ],
    [
      "96933832408409/12769",
      "1112849298702091430940/1442897"
    ],
    [
      "2120449382833269/770884",
      "104921078327459350529265/676836152"
    ],
    [
      "4813930359123021/116281",
      "336894281705000389513080/39651821"
    ]
  ],
  "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. Eight rational points checked exactly; PARI/GP returned rank bounds [8,8]. Rational torsion C4. Source-attributed existing curve.",
  "created_at": "2026-10-21 00:53:20",
  "updated_at": "2026-10-21 00:53:20"
}