{
  "id": 3966,
  "curve_key": "2314519926703569306783936:-84087751040922002419723157727197184",
  "ainvs": [
    "0",
    "0",
    "0",
    "-48219165139657693891332",
    "97323785926993058356161062184256"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2,
    2
  ],
  "naive_height": 168.30373356844817,
  "faltings_height": 12.093516892318057,
  "conductor": "3407621442773364069580883520",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "23",
    "37",
    "59",
    "73",
    "83",
    "89",
    "139",
    "167",
    "239",
    "563",
    "823"
  ],
  "discriminant": "7171191124534007626574866742993557561635141662713075750595801664000000",
  "regulator": "114674744390.52101284866428797149433628266018174618517056",
  "points": [
    [
      "7778220152073/4",
      "-21554422100826575675/8"
    ],
    [
      "46215881954799818/146689",
      "-7146196923209551062174000/56181887"
    ],
    [
      "391267806122",
      "202805570384094240"
    ],
    [
      "-564417356679146551/20866624",
      "3543248810948375708302703355/95318738432"
    ],
    [
      "-874120454600008262/4173849",
      "271030630181083654971590000/8527173507"
    ],
    [
      "-332929719767798/1521",
      "-760812727187362420000/59319"
    ],
    [
      "77587117728321313/338724",
      "6449585674627069310955025/197137368"
    ],
    [
      "1210020727536705/256",
      "-42045569327579962089569/4096"
    ],
    [
      "-2794014736403045743/1193287936",
      "-597651493164215771760537983175/41220938461184"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3676 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 9: 9 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 04:35:52",
  "updated_at": "2026-10-05 04:35:52"
}