{
  "id": 4575,
  "curve_key": "105169170886897:-1078531021806583137481",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2191024393477",
    "1248299611172253249"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 96.85977396263397,
  "faltings_height": 5.582229851399957,
  "conductor": "120716374135263686",
  "bad_primes": [
    "2",
    "13",
    "19",
    "31",
    "37",
    "241",
    "1123",
    "3187"
  ],
  "discriminant": "105234351003688265562972962645504",
  "regulator": "23605.77209750634050597740672639365125900560224601426",
  "points": [
    [
      "784500",
      "110305557"
    ],
    [
      "836642",
      "28233367"
    ],
    [
      "854374",
      "-244225"
    ],
    [
      "866278",
      "18305307"
    ],
    [
      "852142",
      "-4347633"
    ],
    [
      "440834",
      "606484551"
    ],
    [
      "157418",
      "-952598433"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z3.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Seven supplied rational points checked exactly and certified independent modulo torsion. Rational torsion C3. Source-attributed existing curve.",
  "created_at": "2026-10-18 02:10:47",
  "updated_at": "2026-10-18 02:10:47"
}