{
  "id": 3971,
  "curve_key": "185880438189758267536:-2534252913125800521128503361216",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-3872509128953297240",
    "2933163095186438831327607600"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2
  ],
  "naive_height": 140.01490600645988,
  "faltings_height": 9.243833745257774,
  "conductor": "188622615993334511234840880",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "29",
    "31",
    "37",
    "61",
    "79",
    "103",
    "3299",
    "6337",
    "15923"
  ],
  "discriminant": "9876196559540520392216244381899638574382932138496000",
  "regulator": "192415109330809.3257397840313633543404820650899326979313676",
  "points": [
    [
      "18134083902184473/15904144",
      "-14517904073979007318539/63425726272"
    ],
    [
      "2573445496900/1849",
      "1230377942348102080/79507"
    ],
    [
      "121804996579383540/7059649",
      "42245451747689327480909280/18757487393"
    ],
    [
      "1015535620984803788725/760071856041",
      "-7959135043900562930831199056410/662646605605520661"
    ],
    [
      "8675893191530173377/7628974336",
      "5813966590237784649809697/666345134403584"
    ],
    [
      "4781155692333/2209",
      "7110847638042935046/103823"
    ],
    [
      "7007862779658504457/6161622016",
      "-14810180822788644611420827/483662681767936"
    ],
    [
      "2071599777166220481/1821582400",
      "-1232602805642506701955329/77745136832000"
    ],
    [
      "90041844655222242820/69584636521",
      "173016402613031620739325863680/18355661683238069"
    ],
    [
      "176303129516314163031487529332/154999330719300452961",
      "-82281270318745307333176415156533377606368/1929721938985477356083496670959"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3620 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 10: 10 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 04:36:52",
  "updated_at": "2026-10-05 04:36:52"
}