{
  "id": 3996,
  "curve_key": "633704224558994479387077748561:-504463070308517659113171850420005350087684441",
  "ainvs": [
    "1",
    "1",
    "1",
    "-13202171344979051653897453095",
    "583869294338556604550332937455335586810845"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 205.86413950092972,
  "faltings_height": 14.728933836258548,
  "conductor": "142345695678637990158711155259549347070",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "41",
    "43",
    "61",
    "71",
    "89",
    "101",
    "107",
    "241",
    "439",
    "607",
    "2203",
    "2447",
    "75037"
  ],
  "discriminant": "355857877224989486039700387766544387389425496001600122292210470858396875000000000",
  "regulator": "286298674994628003.0744169016659799549771789136795620531277904005",
  "points": [
    [
      "15046041377966340443/6241",
      "-58297327206291039468852339018/493039"
    ],
    [
      "14346890095076674136947/14691889",
      "-1707054281216648227872379352524094/56314010537"
    ],
    [
      "170291530822823",
      "-1809411707178037990362"
    ],
    [
      "242872363599331604932693/3657709441",
      "56008582619219821671188690403982/221214609282239"
    ],
    [
      "95952599458062187/1444",
      "72744812175129262743511/54872"
    ],
    [
      "415314053547461245991323/3317644801",
      "180571374697435624122841437652821862/191093022892799"
    ],
    [
      "212851082197286953276543/2942628516",
      "13702807771664080442159828640625193/159625826478936"
    ],
    [
      "5551146326556325201183/83521321",
      "-1194709600488396193731235957978/763301352619"
    ],
    [
      "416418199222232170939693/6135432241",
      "10426022287095588313380375532586482/480582272005289"
    ],
    [
      "180499858065852590864083/2713263921",
      "-353711272237824201992456431987678/141331204380969"
    ],
    [
      "50023425757490077886890747/476145541089",
      "196157088671283666646354425823225368106/328556136154265937"
    ],
    [
      "157057359253512261242197/2310436489",
      "-2577307459913236263276285380810506/111055750716763"
    ],
    [
      "931122468529649911306765807/14014144141209",
      "62835725890125187411019875272306408274/52462607257390528323"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3636 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 13: 13 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 04:41:59",
  "updated_at": "2026-10-05 04:41:59"
}