{
  "id": 4556,
  "curve_key": "247393:-64041841",
  "ainvs": [
    "1",
    "0",
    "0",
    "-5154",
    "73693"
  ],
  "rank_lower_bound": 7,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 37.25620033283978,
  "faltings_height": 1.1539673405129662,
  "conductor": "6388836643367",
  "bad_primes": [
    "6388836643367"
  ],
  "discriminant": "6388836643367",
  "regulator": "2931.844957771582892012067975355938499585721305532392",
  "points": [
    [
      "11",
      "130"
    ],
    [
      "-23",
      "436"
    ],
    [
      "-9",
      "350"
    ],
    [
      "13",
      "88"
    ],
    [
      "63",
      "-26"
    ],
    [
      "101",
      "715"
    ],
    [
      "68",
      "163"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Michael Rubinstein's elliptic-curves-by-rank repository, records/rank_7.md: https://github.com/mrubinst/elliptic-curves-by-rank. Seven supplied rational points verified exactly and certified independent modulo torsion by quadratic-character 2-descent. Fresh PARI rank bounds [7,7]. Trivial rational torsion. Conductor and minimal discriminant both 6388836643367. Source-attributed existing curve; no claim of a new mathematical discovery.",
  "created_at": "2026-10-18 01:43:01",
  "updated_at": "2026-10-18 01:43:01"
}