{
  "id": 3941,
  "curve_key": "647978152696800270291241:-521603540793413795848087810321109461",
  "ainvs": [
    "1",
    "0",
    "1",
    "-13499544847850005631068",
    "603707801843103968309077094809806"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    6
  ],
  "naive_height": 164.4844318010544,
  "faltings_height": 11.199189134249961,
  "conductor": "1429018850083757362430",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "13",
    "23",
    "31",
    "53",
    "71",
    "191",
    "5557",
    "50131"
  ],
  "discriminant": "10329649883012639247111756273555825572402022794194064239437500",
  "regulator": "168070611.5884032916505896192111950210283799603925435",
  "points": [
    [
      "6159778905717340/91809",
      "-95888878647147213986/27818127"
    ],
    [
      "6709300919199/100",
      "-3142491863040927/1000"
    ],
    [
      "19390311831954/289",
      "20328656215148607/4913"
    ],
    [
      "8859366249988534/131769",
      "3279227350049958128098/47832147"
    ],
    [
      "365488235252584969/419904",
      "219082678459841463108599663/272097792"
    ],
    [
      "27413367519141/400",
      "5231161994183036479/8000"
    ],
    [
      "82489577958532408440/238918849",
      "711315804247013072165723654426/3692968648993"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3718 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 7: 7 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.",
  "created_at": "2026-10-05 04:30:45",
  "updated_at": "2026-10-05 04:30:45"
}