{
  "id": 3978,
  "curve_key": "34810578520974052773178852213209:-117407819084025111322877279451483191621924875677",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-725220385853626099441226087775",
    "135888679495399615706574796105000776535601661"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "naive_height": 217.88242233269057,
  "faltings_height": 16.20143915002896,
  "conductor": "3482515236760862602092865033854708270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "31",
    "59",
    "79",
    "113",
    "173",
    "181",
    "251",
    "1231",
    "330217",
    "25236637"
  ],
  "discriminant": "16434051353085032541995456749719241595533322651472652326633471134668206310957507214945610000",
  "regulator": "11561124087184194.3861251305268400805384068382268884038654720",
  "points": [
    [
      "89873310175354327/529",
      "51018257136786333462928777/12167"
    ],
    [
      "-6197322072811246217/26569",
      "-74049240317197522319968026259/4330747"
    ],
    [
      "14897047826750538063/97969",
      "165497535324163769236297104666/30664297"
    ],
    [
      "16548189298873303665873/17106496",
      "-1303818138892365649928306719965939/70752467456"
    ],
    [
      "1357524819688509290442/724201",
      "45133352758707627700948913319003/616295051"
    ],
    [
      "105413529171940436390673697/12434926144",
      "1076938589557417636113853132452889117293/1386643484169728"
    ],
    [
      "17406862694787002130432751/14593848025",
      "-54845282759193812738382601596982055614/1763009810660125"
    ],
    [
      "8288510874105526830313/43877376",
      "-689876887793675163675713842782331/290643738624"
    ],
    [
      "-1485313019314538765246753/3812939001",
      "-4462808033732284190206910369104403725/235445170372749"
    ],
    [
      "1199491400022817693503169797898/1585065652771689",
      "-285321626776037376709208072775253730626479589/63106033381117879869387"
    ],
    [
      "-12948602965307639228368015729782/21087260013549961",
      "-57261777285116000074253104363876936305587037129/3062176572942711231683291"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3598 (source contributor: dujella). Source equation and witness provenance are credited to that entry. Exact rank 11: 11 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 04:38:22",
  "updated_at": "2026-10-05 04:38:22"
}