{
  "id": 3952,
  "curve_key": "5082644571509211197841:-244679019039811391520088644968889",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-105888428573108566622",
    "283193309100327884365601962221"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2,
    2
  ],
  "naive_height": 149.94035599185233,
  "faltings_height": 10.5271611396818,
  "conductor": "2542465729285305792210",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "31",
    "37",
    "43",
    "103",
    "389",
    "487",
    "140449"
  ],
  "discriminant": "41338852347034765416937809751367732749436365216938297600000000",
  "regulator": "35123287.8081877305329250082450023714422636440802987471",
  "points": [
    [
      "-8082724039",
      "781676886062019"
    ],
    [
      "2029267361",
      "-276901267357581"
    ],
    [
      "-5953978915",
      "-838199284917333"
    ],
    [
      "-41645072181/4",
      "-4056375718879523/8"
    ],
    [
      "27130187585",
      "4168861065617547"
    ],
    [
      "35065719585",
      "6299753306223467"
    ],
    [
      "-20747365271359/8281",
      "550036161383433374649/753571"
    ],
    [
      "487144345629/289",
      "-1625717083104089753/4913"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3667 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 8: 8 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 04:33:09",
  "updated_at": "2026-10-05 04:33:09"
}