{
  "id": 4682,
  "curve_key": "732981001:-19835583599845",
  "ainvs": [
    "1",
    "0",
    "1",
    "-15270438",
    "22956578852"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 61.237891020018424,
  "faltings_height": 2.8479844288961647,
  "conductor": "388521745023566",
  "bad_primes": [
    "2",
    "7",
    "11",
    "41",
    "83",
    "113",
    "401",
    "16361"
  ],
  "discriminant": "203609482740540045092",
  "regulator": "3376.947222895116435160501107062867547413344026943548",
  "points": [
    [
      "-940",
      "191468"
    ],
    [
      "-4174",
      "120320"
    ],
    [
      "-4097",
      "-127389"
    ],
    [
      "3119",
      "73757"
    ],
    [
      "391",
      "-130755"
    ],
    [
      "4043",
      "163231"
    ],
    [
      "-2431",
      "215023"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. I checked the seven supplied rational points exactly on this minimal model. The source records rank 7 with independent points and a matching 2-descent upper bound. Rational torsion Z/2Z. Source-attributed existing curve.",
  "created_at": "2026-10-20 20:35:22",
  "updated_at": "2026-10-20 20:35:22"
}