{
  "id": 3931,
  "curve_key": "-416:2312",
  "ainvs": [
    "0",
    "1",
    "1",
    "9",
    "0"
  ],
  "rank_lower_bound": 3,
  "torsion": [],
  "naive_height": 18.09205578078379,
  "faltings_height": -0.4184860660792147,
  "conductor": "44755",
  "bad_primes": [
    "5",
    "8951"
  ],
  "discriminant": "-44755",
  "regulator": "3.2697796220947170124103261879643568792077733",
  "points": [
    [
      "0",
      "0"
    ],
    [
      "2",
      "5"
    ],
    [
      "10",
      "34"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Known curve Cremona 44755a1, with original generator provenance from John Cremona's ecdata. Exact rank 3 confirmed by explicit independent points and a matching PARI/GP ellrank upper bound. This fills a gap in this leaderboard; no claim of a previously unknown mathematical curve.",
  "created_at": "2026-10-05 04:28:33",
  "updated_at": "2026-10-05 04:28:33"
}