{
  "id": 5877,
  "curve_key": "99721119216:-11287430685362520",
  "ainvs": [
    "0",
    "0",
    "1",
    "-2077523317",
    "13064155885836"
  ],
  "rank_lower_bound": 13,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 75.97692995737448,
  "faltings_height": 4.391342114880528,
  "conductor": "500145136377795551079641841157",
  "bad_primes": [
    "544889",
    "73250531",
    "12530754803850223"
  ],
  "discriminant": "500145136377795551079641841157",
  "regulator": "2628623436.413143046062722771596341243357205711836322971113518944",
  "points": [
    [
      "5814",
      "1087181"
    ],
    [
      "-46469",
      "3043175"
    ],
    [
      "-36326",
      "6371598"
    ],
    [
      "-21751",
      "6925448"
    ],
    [
      "-44268",
      "-4275736"
    ],
    [
      "24497/4",
      "-6042957/8"
    ],
    [
      "-7044",
      "5229600"
    ],
    [
      "149986",
      "55457369"
    ],
    [
      "1207",
      "3249360"
    ],
    [
      "43193",
      "-1977897"
    ],
    [
      "-2267",
      "4214528"
    ],
    [
      "-39801",
      "5718576"
    ],
    [
      "68828",
      "14004671"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Source: Michael Rubinstein’s elliptic-curves-by-rank repository, rank_13.add_2026-10-24.tsv.gz, 52nd 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 500145136377795551079641841157. The construction author and search method are not identified in the source row.",
  "created_at": "2026-10-25 19:07:29",
  "updated_at": "2026-10-25 19:07:29"
}