{
  "id": 3974,
  "curve_key": "2467977284489695081:-3866259339703043690670258229",
  "ainvs": [
    "1",
    "0",
    "1",
    "-51416193426868648",
    "4474837194445691856407078"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2
  ],
  "naive_height": 127.04979172763426,
  "faltings_height": 8.400065530255963,
  "conductor": "10817942205250900617851910",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "61",
    "83",
    "131",
    "191",
    "229",
    "349",
    "359",
    "479",
    "991"
  ],
  "discriminant": "48767865638933426457990098696762940018716306250000",
  "regulator": "28184030706319.19929560669323269200220122964074474912346892",
  "points": [
    [
      "3728644669/25",
      "-44025816791513/125"
    ],
    [
      "7204437715069/52441",
      "-769667763938893045/12008989"
    ],
    [
      "231425960463344026/1690607689",
      "2805927329310308829728035/69512716348613"
    ],
    [
      "287127052354/1681",
      "56656290818169070/68921"
    ],
    [
      "1847716232367154/6528025",
      "59196693618453124437082/16679103875"
    ],
    [
      "680325699811785673/3646831321",
      "258256886445222464960433547/220228496643869"
    ],
    [
      "1681398488830777/11744329",
      "-8838844801334167482691/40247815483"
    ],
    [
      "32584108361939766867949/133430660385961",
      "3923851537008056754668573990824205/1541286779432860036459"
    ],
    [
      "282811541717393837784781/537961496836009",
      "138229795535554936534291548236281235/12477477343729902237973"
    ],
    [
      "51167670777092848463879401/32643887991289",
      "366010288580141107375505518131970803365/186510299092133849587"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3618 (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 04:37:36",
  "updated_at": "2026-10-05 04:37:36"
}