{
  "id": 3953,
  "curve_key": "3045533277440444226849:-168071863845608000520022993378257",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-63448609946675921393",
    "194527620207538079014473370832"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2,
    2
  ],
  "naive_height": 148.40388891260196,
  "faltings_height": 9.846281927177802,
  "conductor": "18082853740749081030705",
  "bad_primes": [
    "3",
    "5",
    "7",
    "19",
    "43",
    "89",
    "167",
    "227",
    "257",
    "1429",
    "8101"
  ],
  "discriminant": "573929210151589088910311287950787405196654591926700625",
  "regulator": "3373374740.68665918549977790661182070499554576465993958",
  "points": [
    [
      "654642100293/121",
      "-130533406396844977/1331"
    ],
    [
      "7364097795937/1089",
      "-9821980788792588929/35937"
    ],
    [
      "75511864957/16",
      "910609733038833/64"
    ],
    [
      "560214057577/121",
      "-4855264325605975/1331"
    ],
    [
      "125664244054969/27225",
      "8910460212489824123/4492125"
    ],
    [
      "26570723206533/5776",
      "62699256208457083/438976"
    ],
    [
      "10171921392897/2209",
      "-71953568091585991/103823"
    ],
    [
      "44065170048463/8836",
      "38393764234633485697/830584"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3671 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 8: 8 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 04:33:24",
  "updated_at": "2026-10-05 04:33:24"
}