{
  "id": 3945,
  "curve_key": "809821814658965073:-444048763680956155276498905",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-16871287805395106",
    "513945332552261945881761"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2,
    2
  ],
  "naive_height": 123.70677190942527,
  "faltings_height": 8.349452985621474,
  "conductor": "496764009210534318",
  "bad_primes": [
    "2",
    "3",
    "11",
    "37",
    "41",
    "67",
    "73",
    "4523",
    "74761"
  ],
  "discriminant": "193235561581907532217840601098339123129327362084864",
  "regulator": "6014911608.429800512933460634109053048400398439579980",
  "points": [
    [
      "166576821093/121",
      "-67690726747844267/1331"
    ],
    [
      "-9356044990109182455231/76257237386521",
      "571737375252455353025894579198445/665919299510052706819"
    ],
    [
      "37159323122465/1151329",
      "-68161352709512762481/1235376017"
    ],
    [
      "251624476757/16129",
      "1033428411836537529/2048383"
    ],
    [
      "10355915361394209/49126081",
      "865928176187695941294815/344324701729"
    ],
    [
      "7096992726250561/3448449",
      "-596708867834163692935585/6403769793"
    ],
    [
      "3480468558382596563140669043187415/2087471514642766101093924",
      "204716849691250783859691565860480842194147255014251/3015996524993275848361531260807196968"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3660 (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 04:31:41",
  "updated_at": "2026-10-05 04:31:41"
}