{
  "id": 4016,
  "curve_key": "4633446059960809002319924781867081425:-2425286266012202885552380064916004728127860514202025625",
  "ainvs": [
    "1",
    "0",
    "0",
    "-96530126249183520881665099622230863",
    "2807044289365975553937744183998600954453672848844217"
  ],
  "rank_lower_bound": 16,
  "torsion": [
    2
  ],
  "naive_height": 253.2790926853385,
  "faltings_height": 19.171137680432658,
  "conductor": "4037723001611237548976485813408801349432131894744731730350",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "41",
    "71",
    "79",
    "97",
    "151",
    "163",
    "179",
    "191",
    "193",
    "199",
    "239",
    "811",
    "1481",
    "2179",
    "21563",
    "392599",
    "438143597"
  ],
  "discriminant": "54162394123530447580495431211861592641810856611752338287754644006540014584740860107365739415831494229000000",
  "regulator": "399963582110715549094135.0263788557559309444176558671744528184940495006",
  "points": [
    [
      "-7105362832321028105082/22201",
      "100268890496448143625511487342673/3307949"
    ],
    [
      "-614369822703161280465318/2468041",
      "414181996909057787459204845701951639/3877292411"
    ],
    [
      "-12353346368233147995918/73441",
      "2378738543287396072386135734792139/19902511"
    ],
    [
      "1036679554974304734928662/2211169",
      "-809443080191528589922764630911881365/3288008303"
    ],
    [
      "125541706601867236672899/386884",
      "18090969462881509425228308991509157/240641848"
    ],
    [
      "501847207962575734758/841",
      "9684892748914502194165041442185/24389"
    ],
    [
      "-1490827542485623242869876523/47927717776",
      "797679828878370945997541117260007470998201/10492527686393024"
    ],
    [
      "-3926786670730567232901282444/44909662561",
      "978881409351463034637371832278578788911091/9517210780264559"
    ],
    [
      "-187928673333035798342634/4289041",
      "740645641813490832732969340127596755/8882603911"
    ],
    [
      "18912837763813994553/64",
      "-4794559726244801972698095087/512"
    ],
    [
      "19770951147621553898765056758/66552132529",
      "320384343939050750624900365848873638626317/17168919493433833"
    ],
    [
      "419034589192420139604593928/14827689361",
      "-18203536215672747422241608693402758419045/1805552905799609"
    ],
    [
      "-467395083932018171355961863712202/11203927603840449",
      "-97515508429899706867729184930520460987032401379893/1185920129795359376904543"
    ],
    [
      "2276483786689133105945868/923521",
      "-3407695600544965411591571444296101273/887503681"
    ],
    [
      "179916621814596275162266438/236759769",
      "2210796680776109523262984736991648306047/3643022565603"
    ],
    [
      "-1474148834151299575062877264308792/13864891292028529",
      "-177857258204470992026448353437037062692776345210067/1632580869860389985009417"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3654 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 16: 16 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 04:46:28",
  "updated_at": "2026-10-05 04:46:28"
}