{
  "id": 3965,
  "curve_key": "3010610945798250445646433:2385661202967345231047720954079156975",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-62721061370796884284301",
    "-2761181947863191529851422253557579"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2,
    2
  ],
  "naive_height": 169.09255578614352,
  "faltings_height": 12.145205424529326,
  "conductor": "4145713793217534004171727022",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "19",
    "37",
    "47",
    "59",
    "73",
    "107",
    "827",
    "1031",
    "3517",
    "5039"
  ],
  "discriminant": "12497760813342119729665870577812294292331107581497731870516243966459904",
  "regulator": "73151550727.160258127226369828350669856114347752937999070",
  "points": [
    [
      "1878030396831",
      "-2550149274655697240"
    ],
    [
      "785142030767296719/1181569",
      "640853133847148687304006664/1284365503"
    ],
    [
      "3509707282776921/3136",
      "-202441898776295493643777/175616"
    ],
    [
      "50047231437579/169",
      "-149577902725131613244/2197"
    ],
    [
      "1123416623636621211/534361",
      "1182067095236519443910341160/390617891"
    ],
    [
      "7705687900878679/841",
      "676167010224193683938120/24389"
    ],
    [
      "32370128042397231/58081",
      "5150554722937941040675960/13997521"
    ],
    [
      "51532704806791791/185761",
      "2760122560674501238657160/80062991"
    ],
    [
      "1519280695614890999919/53919649",
      "-59216111846654864855083442017144/395931982607"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3679 (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 04:35:42",
  "updated_at": "2026-10-05 04:35:42"
}