{
  "id": 6079,
  "curve_key": "28891277973083961:-6139389204892383252002541",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-601901624439249",
    "7105774693174923762593"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 114.15353498207465,
  "faltings_height": 7.51900998667474,
  "conductor": "247764568508053377686010",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "31",
    "41",
    "71",
    "97",
    "137",
    "193",
    "919",
    "205441"
  ],
  "discriminant": "-7856700455161951046484574579415120236519120500",
  "regulator": "963070.23434166526924586536750290343881806585114989462046",
  "points": [
    [
      "14971192",
      "38073765199"
    ],
    [
      "265119244",
      "4298970608941"
    ],
    [
      "47954242",
      "297495869149"
    ],
    [
      "-22458446",
      "-96404112395"
    ],
    [
      "57802652",
      "406715975709"
    ],
    [
      "376680247/4",
      "-7090763693257/8"
    ],
    [
      "41680327",
      "-233317755536"
    ],
    [
      "-7137853",
      "105067329984"
    ],
    [
      "21508162",
      "-64117498271"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Original search by mpjunior92 (2026), public Yukon elliptic-rank challenge submission 511c1096-00f9-44d6-ac2b-f25c14268cf9. Source: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/5a6292b9ab454208976b6c1de8f1e2a1ef854da4/submission/board/3-9.ec . The source used a Mestre-Nagao sieve in the Z/3 Tate family y^2 + a*x*y + b*y = x^3 with (a,b) = (8121,-125917328145). The nine supplied points have been checked exactly on the minimal model and certified independent modulo torsion by an exact rank-9 F_5 reduction matrix at nine good primes.",
  "created_at": "2026-10-29 00:39:38",
  "updated_at": "2026-10-29 00:39:38"
}