{
  "id": 4599,
  "curve_key": "77067217:-1013169887929",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1605567",
    "1172516536"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 55.28821006972451,
  "faltings_height": 2.6366586254548117,
  "conductor": "329157169581291693751",
  "bad_primes": [
    "329157169581291693751"
  ],
  "discriminant": "-329157169581291693751",
  "regulator": "2124380.568934963282237815562579114793011904092051441806215",
  "points": [
    [
      "569",
      "20769"
    ],
    [
      "-648",
      "44380"
    ],
    [
      "-1480",
      "-16796"
    ],
    [
      "-1469",
      "19750"
    ],
    [
      "1295",
      "-36221"
    ],
    [
      "-1531",
      "7294"
    ],
    [
      "1400",
      "-41556"
    ],
    [
      "3780",
      "219734"
    ],
    [
      "1617",
      "52153"
    ],
    [
      "-49",
      "-35346"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Michael Rubinstein's elliptic-curves-by-rank repository, rank_10.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Ten supplied rational points checked exactly and certified independent modulo torsion. Rational torsion trivial. Source-attributed existing curve.",
  "created_at": "2026-10-18 22:30:07",
  "updated_at": "2026-10-18 22:30:07"
}