{
  "id": 3957,
  "curve_key": "12541176249468391470189264929909113356961:-1010672665644870184975308968949576121581836469137945607197041",
  "ainvs": [
    "1",
    "0",
    "0",
    "-261274505197258155628943019373106528270",
    "1169760029681562714070019912702978627750639550628567056900"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    6
  ],
  "naive_height": 276.98950787211527,
  "faltings_height": 21.107633353628078,
  "conductor": "11562784654375022501788319763332764230",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "29",
    "37",
    "43",
    "67",
    "113",
    "419",
    "421",
    "677",
    "4639",
    "52081",
    "87421"
  ],
  "discriminant": "550365034897143495624094836456818932672813714435075450998615205649043737983621940843228783877808784024137781328192000",
  "regulator": "255249094490.37602848390761482171712973327985715038968984",
  "points": [
    [
      "24886090592368449580",
      "100399454956338682280050118290"
    ],
    [
      "189317464585511304165911624560/3951505321",
      "78007522417132566931229801603987384222545130/248395575983381"
    ],
    [
      "313986353115953192721113380/6046681",
      "5311710376202265530334920914686939163310/14868788579"
    ],
    [
      "2190678091046096831371534/162409",
      "-653506634721959829747958512211966796/65450827"
    ],
    [
      "1647063672086135566748050/961",
      "2113714457871121122511792899854368120/29791"
    ],
    [
      "60396081551009096679268/4489",
      "-2852502756641914790200162840581794/300763"
    ],
    [
      "2320297182422620021630/49",
      "105707234115983425107242438874250/343"
    ],
    [
      "80958606286245429715840296/801025",
      "719482887277826439307083078684555381834/716917375"
    ],
    [
      "569378578337821202394930055/42276004",
      "2663221300662040818179259246980352256975/274878578008"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3834 (source contributor: dujella). Source equation and witness provenance are credited to that entry. Exact rank 9: 9 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 04:34:06",
  "updated_at": "2026-10-05 04:34:06"
}