{
  "id": 3979,
  "curve_key": "24433022388279901981216348854673:-96034655024262866851688612752204793321629113785",
  "ainvs": [
    "1",
    "1",
    "1",
    "-509021299755831291275340601139",
    "111151221092896624541690625755717516434042481"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "naive_height": 216.8204651511023,
  "faltings_height": 16.078186822215265,
  "conductor": "27145429606258964067875985943433158218",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "17",
    "19",
    "23",
    "103",
    "1063",
    "6673",
    "43801",
    "76441",
    "1625287",
    "1683223"
  ],
  "discriminant": "3103697639258640422000292758398416206001431250963213987009342036381344363679941004939300864",
  "regulator": "1802137171296770.69510759650887893800781808223482426049360312",
  "points": [
    [
      "17173919075106975/361",
      "-63992347597495589314680782/6859"
    ],
    [
      "23032874262803275/9",
      "-3369067144167854551518646/27"
    ],
    [
      "-508257524050473098721/697225",
      "-5669564725966450137578975474378/582182875"
    ],
    [
      "6651262448027715219/30625",
      "17648737777882372740712762978/5359375"
    ],
    [
      "-9647460810771565773/152881",
      "-714876116876242922877608372318/59776471"
    ],
    [
      "-7505832468440628262929/14707225",
      "-870141737480050514756955139257086/56402207875"
    ],
    [
      "2375207556564020128327/3876961",
      "41285302049229108340528366629878/7633736209"
    ],
    [
      "803962337910917113069791/4628761225",
      "1665789358793406700449900685565735506/314917769942875"
    ],
    [
      "1278520983170868265268299/2134902025",
      "-453044534141004393641874324330855242/98643148065125"
    ],
    [
      "129201686003041749452880823/523174129",
      "1468589640166001412891727497450993953990/11966561852617"
    ],
    [
      "-6651223221016905641584914968349825/8847101826137811721",
      "-218456973748942021813869640192083223242981387205358/26314888776376671145389752731"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3518 (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 04:38:33",
  "updated_at": "2026-10-05 04:38:33"
}