{
  "id": 3962,
  "curve_key": "88490004090754188454537201:-829813260811132281814891592147799245801",
  "ainvs": [
    "1",
    "1",
    "1",
    "-1843541751890712259469525",
    "960432014826931257852095990433322010"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2,
    2
  ],
  "naive_height": 179.23479548809436,
  "faltings_height": 12.753111998754973,
  "conductor": "6830331854767804004039231385",
  "bad_primes": [
    "3",
    "5",
    "11",
    "13",
    "17",
    "31",
    "41",
    "43",
    "73",
    "103",
    "127",
    "443",
    "821",
    "941",
    "10487"
  ],
  "discriminant": "2505342782817127150084980658321288763905817358738160710174995931908765625",
  "regulator": "101912616849.21663047909536922845312150662142299639349576",
  "points": [
    [
      "717587027433",
      "-83894796137064317"
    ],
    [
      "20181656783750103/2116",
      "-2839452259710522641758187/97336"
    ],
    [
      "3511892478933",
      "-6148143500458258067"
    ],
    [
      "95541170887963/36",
      "-829850213347091245597/216"
    ],
    [
      "149310645003559483/181476",
      "-1883050688602579241005367/77308776"
    ],
    [
      "-20261165574471093/33124",
      "-8220156565202685941518381/6028568"
    ],
    [
      "-35549389952523/49",
      "-474785953760879729681/343"
    ],
    [
      "330764022597537/169",
      "4838092243340016794251/2197"
    ],
    [
      "171495280535824155553/207965241",
      "92606529057432838939789250863/2999066740461"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3680 (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 04:35:07",
  "updated_at": "2026-10-05 04:35:07"
}