{
  "id": 3967,
  "curve_key": "86599999593424855610375370400225:256375328635526063889793224831461104947376403375",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1804166658196351158549486883338",
    "-296730704439266427997445156213824676516703708"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2,
    2
  ],
  "naive_height": 220.61655780208469,
  "faltings_height": 16.446498698814278,
  "conductor": "749928839103528874724228030523150",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "41",
    "47",
    "53",
    "71",
    "151",
    "179",
    "449",
    "4157",
    "10357",
    "44893"
  ],
  "discriminant": "337808783402559017824865234546494336353577625346804136811700506123270218823096293689600000000",
  "regulator": "470333555414964.4964860333532486060450867149419614307160244",
  "points": [
    [
      "-29874286575994284/121",
      "-15387816062028928552242606/1331"
    ],
    [
      "5549960369431476",
      "400799733635999275643430"
    ],
    [
      "-12455555654165326195938569598924/23004420154870561",
      "79670783933251322390347638965965197406541557830/3489128277087560272507441"
    ],
    [
      "350757137307823887683586838068/78835770860401",
      "197675004309685253828902405950607627114303530/699978946516728319351"
    ],
    [
      "-38757311934952937326641842/77458125969",
      "-472665814468916151466568723282807077352/21557603412810297"
    ],
    [
      "-6355362920616297309223548/14615117449",
      "-35583003718873875871318880316988517826/1766865393761957"
    ],
    [
      "2698276073385246069852/961",
      "140161754000766450855423459292794/29791"
    ],
    [
      "-2653031465383229961352268/13712175801",
      "-10782796800579185102594328580302734734/1605682074121299"
    ],
    [
      "873229762539226811870443678644/114940334166529",
      "-802869704356977885563339751444805959264612390/1232277966227043239167"
    ],
    [
      "441577460060214738359364/141300769",
      "263362704734592563402542722534151290/1679642241103"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3696 (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 04:36:03",
  "updated_at": "2026-10-05 04:36:03"
}