{
  "id": 3981,
  "curve_key": "1537535999747239762561:36546705482666309080443015299135",
  "ainvs": [
    "1",
    "0",
    "0",
    "-32031999994734161720",
    "-42299427644644228101925781184"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2
  ],
  "naive_height": 146.3534042633074,
  "faltings_height": 10.23702569997586,
  "conductor": "2681265063185100898944986344566",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "23",
    "61",
    "73",
    "127",
    "173",
    "457",
    "631",
    "3607",
    "1787719"
  ],
  "discriminant": "1330497386457469064100801674266421983703188925211595834436352",
  "regulator": "176779756449859.955142672897863074650790576624021511675349752",
  "points": [
    [
      "-263324735074472/58081",
      "1381107152388335992744/13997521"
    ],
    [
      "-48997164843806/15625",
      "-322774028118762620878/1953125"
    ],
    [
      "-197638453599944/58081",
      "-2312655485905055696864/13997521"
    ],
    [
      "343058104186",
      "-200905838536595294"
    ],
    [
      "4709367023331256/654481",
      "167241967052727067372832/529475129"
    ],
    [
      "130909691953864/11449",
      "1276828478117179556144/1225043"
    ],
    [
      "-10226969137981962/6661561",
      "981459751263936620127534/17193488941"
    ],
    [
      "-1863842489626604/990025",
      "104864913070403036061884/985074875"
    ],
    [
      "31260600487973736/4084441",
      "-3310829733935214055661112/8254655261"
    ],
    [
      "897022694668881832/31281649",
      "832089671943545076248006896/174958262857"
    ],
    [
      "1412140645306984/2209",
      "53063953303454851132184/103823"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3628 (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 04:38:54",
  "updated_at": "2026-10-05 04:38:54"
}