{
  "id": 3970,
  "curve_key": "637793870724007007927251248:8200214890946291517434090798262042608640",
  "ainvs": [
    "0",
    "0",
    "0",
    "-13287372306750145998484401",
    "-9490989457113763330363531016506993760"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2,
    2
  ],
  "naive_height": 185.160172129076,
  "faltings_height": 13.480241427736273,
  "conductor": "282976117803100217896404857655264",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "29",
    "31",
    "43",
    "59",
    "61",
    "67",
    "83",
    "107",
    "113",
    "151",
    "277",
    "4397",
    "7417"
  ],
  "discriminant": "111226225696164027935178300642208489334940868631883504691098151847176109081664",
  "regulator": "13427262305383.39349494891248558596752525882550930073143874",
  "points": [
    [
      "-4692239022559/4",
      "-16935984631109460105/8"
    ],
    [
      "-219564008353680345639/82537225",
      "1988289968905138614342839916484/749850689125"
    ],
    [
      "-931649989453865431/297025",
      "186506551947909316992229872/161878625"
    ],
    [
      "-1973966141272687551/839056",
      "2273199993480150220327755745/768575296"
    ],
    [
      "-380131350726639/484",
      "-7224831844430105142895/10648"
    ],
    [
      "75078508596117630689/10758400",
      "-543983453058207051891100579887/35287552000"
    ],
    [
      "-1752407740492373532639/2084379025",
      "-99165080053244373793761711475516/95162324386375"
    ],
    [
      "3926053808785338681/336400",
      "7365528892463903383386766829/195112000"
    ],
    [
      "-223612618995498039/80656",
      "-56283649127264464581006715/22906304"
    ],
    [
      "-2175298025829624452468131135/2582242379061361",
      "-137908708895650331213926753433144802976980/131218632236392557401609"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3695 (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 04:36:42",
  "updated_at": "2026-10-05 04:36:42"
}