{
  "id": 5878,
  "curve_key": "80877321616:-44372704090632920",
  "ainvs": [
    "0",
    "-1",
    "1",
    "-1684944200",
    "51357858049262"
  ],
  "rank_lower_bound": 13,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 76.66280180513026,
  "faltings_height": 4.432546583034581,
  "conductor": "277759817061511866219351665481",
  "bad_primes": [
    "3",
    "4793",
    "19317046878191241826229339"
  ],
  "discriminant": "-833279451184535598658054996443",
  "regulator": "41438840888.40117611165715061838552223574029150088589268732134193",
  "points": [
    [
      "-51668",
      "693477"
    ],
    [
      "-49202",
      "3892049"
    ],
    [
      "-39814",
      "7438366"
    ],
    [
      "-38185",
      "7747171"
    ],
    [
      "-36320",
      "8040053"
    ],
    [
      "-2493",
      "7452712"
    ],
    [
      "3014",
      "6804910"
    ],
    [
      "6398",
      "6390574"
    ],
    [
      "11431",
      "5795756"
    ],
    [
      "11816",
      "5753098"
    ],
    [
      "26316",
      "5024026"
    ],
    [
      "74474",
      "18410014"
    ],
    [
      "-429056/9",
      "130428046/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Source: Michael Rubinstein’s elliptic-curves-by-rank repository, rank_13.add_2026-10-24.tsv.gz, 31st data row, pinned at commit 5e2e867ddb468765263bfadf520d9acda17a5a4b:\r\nhttps://raw.githubusercontent.com/mrubinst/elliptic-curves-by-rank/5e2e867ddb468765263bfadf520d9acda17a5a4b/rank_13.add_2026-10-24.tsv.gz\r\n\r\nThe source row reports proven rank 13 and supplies these 13 generators on the minimal model. I checked all 13 points exactly and independently verified their independence, establishing rank at least 13. Trivial torsion; conductor 277759817061511866219351665481. The construction author and search method are not identified in the source row.",
  "created_at": "2026-10-25 19:11:16",
  "updated_at": "2026-10-25 19:11:16"
}