{
  "id": 3954,
  "curve_key": "1241511466240729404553:28957470625029077504113283736155",
  "ainvs": [
    "1",
    "0",
    "1",
    "-25864822213348529262",
    "-33515591003346463777169418800"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2,
    2
  ],
  "naive_height": 145.71184954378316,
  "faltings_height": 10.17664761622554,
  "conductor": "19479441722836754745294",
  "bad_primes": [
    "2",
    "3",
    "13",
    "17",
    "29",
    "83",
    "179",
    "373",
    "863",
    "5099",
    "20773"
  ],
  "discriminant": "622146694665010005697831715784995712062805234047697654387984",
  "regulator": "671150643.743883984209633493166242965351535003561773099",
  "points": [
    [
      "-5630685077386/1369",
      "2904588261899893737/50653"
    ],
    [
      "-3281445919",
      "-126585026808651"
    ],
    [
      "-20796139455922183/6205081",
      "1925921785320778078334331/15456856771"
    ],
    [
      "-1302954307940423/553536",
      "49290940875065540139169/411830784"
    ],
    [
      "-184870211818/49",
      "-34918143187608981/343"
    ],
    [
      "-234026302747/121",
      "-128180408590607877/1331"
    ],
    [
      "-265249184647/121",
      "-149695889544794997/1331"
    ],
    [
      "4304873183801/121",
      "-8836767881462804661/1331"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3672 (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 04:33:34",
  "updated_at": "2026-10-05 04:33:34"
}