{
  "id": 3992,
  "curve_key": "161397364889012919084801:-64828190924116903858875330509154945",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-3362445101854435814267",
    "75032628385235175926939685931755"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "naive_height": 160.31446914597447,
  "faltings_height": 11.074976830990476,
  "conductor": "3744534523427843486091406117969518",
  "bad_primes": [
    "2",
    "3",
    "11",
    "29",
    "31",
    "37",
    "163",
    "167",
    "199",
    "491",
    "1237",
    "2063",
    "3137",
    "4933",
    "5413"
  ],
  "discriminant": "904673183445661196541777760392525691645178617711431144600523392",
  "regulator": "720319151239051.78951140177746382471595320932957693277183370743",
  "points": [
    [
      "69023561283",
      "-13106915664976758"
    ],
    [
      "26538999992728163/591361",
      "-1732759769219313830492334/454756609"
    ],
    [
      "48634385135",
      "5151408072971910"
    ],
    [
      "71632456803",
      "14203256845273674"
    ],
    [
      "504631173893",
      "356207396977413924"
    ],
    [
      "960853127431727/9409",
      "-25759997968228080004794/912673"
    ],
    [
      "38351082900174595/314721",
      "-6780366520307267860196366/176558481"
    ],
    [
      "73052849891957700943/1256773401",
      "-388367820929274125358883923926/44553873838851"
    ],
    [
      "14051765332615/9",
      "-52638203862679316542/27"
    ],
    [
      "350668205755/9",
      "-48089100248422322/27"
    ],
    [
      "21632598858437/529",
      "29592331769530320474/12167"
    ],
    [
      "24265593349145621/648025",
      "665785225848204423507804/521660125"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3632 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 12: 12 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 04:41:06",
  "updated_at": "2026-10-05 04:41:06"
}