{
  "id": 1803,
  "curve_key": "162386139137408102040425018031563200:-65436996053492878952090383882152333783682129068160000",
  "ainvs": [
    "0",
    "1",
    "0",
    "-3383044565362668792508854542324233",
    "75737263950801942103904570668638566598532431572663"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "naive_height": 243.22585542824834,
  "faltings_height": 17.798266509650674,
  "conductor": "207871256848409744593342350561253204800",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "23",
    "37",
    "41",
    "101",
    "359",
    "389",
    "541",
    "12479",
    "23209",
    "49411",
    "51431"
  ],
  "discriminant": "911981998986183047761413416183206545752553412386768512865668602893397070733232542617096256000000",
  "regulator": "348545797296.277062008862168967922814386554169478065932579861",
  "points": [
    [
      "21966937543749263",
      "3467304529380020399592600"
    ],
    [
      "33560959657313363",
      "5137371389991712861800"
    ],
    [
      "34582038915915083",
      "319292566508771961823200"
    ],
    [
      "134483428957332077/4",
      "96800241541200000930525/8"
    ],
    [
      "31780818196317203",
      "566228347995386167907400"
    ],
    [
      "1413627031281777887/49",
      "502860429284713027048333800/343"
    ],
    [
      "9700355475181684787/289",
      "16274604587975225427493800/4913"
    ],
    [
      "33623189883813803",
      "12873137085655241194800"
    ],
    [
      "33548281734503453",
      "9678428398238096687400"
    ],
    [
      "173923494287946441475667/2809",
      "72533258254815185975583870670539600/148877"
    ],
    [
      "-2251179780875766539120038/34421689",
      "839055527133163935536879014270829625/201952049363"
    ]
  ],
  "submitter": "hdeping",
  "history": [],
  "commentary": "Rank 11 with torsion Z/2Z x Z/2Z induced by a rational Diophantine triple, smallest known conductor in its class (Dujella-Peral 2017/2020); witness points from the paper.",
  "created_at": "2026-09-25 15:05:28",
  "updated_at": "2026-09-25 15:05:28"
}