{
  "id": 3986,
  "curve_key": "6665657260596459961:-1060272272390527140761438765",
  "ainvs": [
    "1",
    "1",
    "0",
    "-138867859595759582",
    "1227166924071872322092580"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2
  ],
  "naive_height": 130.03050070921316,
  "faltings_height": 8.903884490600069,
  "conductor": "672519215577201888821790774558",
  "bad_primes": [
    "2",
    "3",
    "11",
    "41",
    "53",
    "61",
    "71",
    "89",
    "103",
    "191",
    "499",
    "1013",
    "5653"
  ],
  "discriminant": "170739324019474751329036099245369612564375238837732752",
  "regulator": "56274266480667.2845464137010321755341309821676230521866278494",
  "points": [
    [
      "-195710674916696/528529",
      "526282792526149196150/384240583"
    ],
    [
      "-778453226219/2809",
      "639115910449271499/148877"
    ],
    [
      "4210956285852136/41209",
      "273254632039838121956634/8365427"
    ],
    [
      "-25284927119411/73441",
      "57091307881770777444/19902511"
    ],
    [
      "-17336730037533791/157552704",
      "7704001034940032666506627/1977601540608"
    ],
    [
      "86520551464/169",
      "-17619901521977962/2197"
    ],
    [
      "-433820928731/1369",
      "-185490671708750853/50653"
    ],
    [
      "43418873604934024/82609921",
      "-6434279369442195122134562/750841571969"
    ],
    [
      "683398000022790676/1076430481",
      "-459071868233538669559628074/35316607651129"
    ],
    [
      "3206945868456/3481",
      "5257018378097333646/205379"
    ],
    [
      "11851844992423621/8497225",
      "-1243682238468231905135964/24769410875"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3624 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 11: 11 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 04:39:53",
  "updated_at": "2026-10-05 04:39:53"
}