{
  "id": 3985,
  "curve_key": "29438862457199653561:-159726768745557447872039853485",
  "ainvs": [
    "1",
    "1",
    "0",
    "-613309634524992782",
    "184868945051812476207225060"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2
  ],
  "naive_height": 134.48654198293667,
  "faltings_height": 8.83209721981726,
  "conductor": "686044836958354728450143389446",
  "bad_primes": [
    "2",
    "3",
    "11",
    "17",
    "31",
    "101",
    "157",
    "199",
    "347",
    "487",
    "593",
    "2351"
  ],
  "discriminant": "260458878016993866992898967860704696649784248398352",
  "regulator": "288944231484399.614624938973452184543366475603273522971798639",
  "points": [
    [
      "195646059049/256",
      "-52218751204640083/4096"
    ],
    [
      "558815915714749/1229881",
      "-97339639877793743717/1363938029"
    ],
    [
      "31354794783096/69169",
      "-259805569175373582/18191447"
    ],
    [
      "4651068288696/10201",
      "137870294263773990/1030301"
    ],
    [
      "3299431628056/7225",
      "99265919790693666/614125"
    ],
    [
      "7434901164178215651648061/13642478973846529",
      "-5631610482506117227588055419204110876/1593455500401264832199167"
    ],
    [
      "144678832271416/231361",
      "-753819451289539471266/111284641"
    ],
    [
      "69764959984861/145161",
      "58514659398909635555/55306341"
    ],
    [
      "22944435061/49",
      "-204291996614644/343"
    ],
    [
      "776743839583648216/1711725129",
      "-3171676775558318601968366/70819203762117"
    ],
    [
      "86614103340799952929/190969000000",
      "-2717904067156517833138182717/83453453000000000"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3625 (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 04:39:43",
  "updated_at": "2026-10-05 04:39:43"
}