{
  "id": 3226,
  "curve_key": "164738686335314937734966418081395641:-52937069318451125686912044578227268908536469272358189",
  "ainvs": [
    "1",
    "0",
    "1",
    "-3432055965319061202811800376695743",
    "61269756155614728518291684114878312854267178414658"
  ],
  "rank_lower_bound": 16,
  "torsion": [
    2
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  "naive_height": 243.26900570434591,
  "faltings_height": 18.28306386747029,
  "conductor": "53142274232491098392872393941753394804628410908321062888347710",
  "bad_primes": [
    "2",
    "3",
    "5",
    "29",
    "31",
    "41",
    "59",
    "89",
    "107",
    "113",
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    "577",
    "1009",
    "1123",
    "1193",
    "1433",
    "1523",
    "1873",
    "3881",
    "58549"
  ],
  "discriminant": "965557107383163947330266571531075387575273342835948360762619236684572481676928760057195262520556250000",
  "regulator": "4583088397164293.410590750293736906189906919849130157258410015280381031",
  "points": [
    [
      "52359749829117744",
      "-5011456011734531643879410"
    ],
    [
      "7195374267770659659/361",
      "6062270165442648153955195660/6859"
    ],
    [
      "236115388568601561399/3721",
      "2258329803580867130530672993840/226981"
    ],
    [
      "50703358678534041/64",
      "-3917761687638900073132536745/512"
    ],
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      "-11476820464091303908997671824/2146743641329",
      "-28038767068883385550809975218807601260699255/3145359408171500233"
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      "2368063282069676256/49",
      "986945335955161282760861170/343"
    ],
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      "-2447387879479090328559/43264",
      "-77618369283490231354575667023695/8998912"
    ],
    [
      "3050112828892045803/3721",
      "1735433288646828013638157161268/226981"
    ],
    [
      "1855894021744395939",
      "-2527058887223660374495154300"
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      "1433203571646947868107861195468691/5925086428023889",
      "-52763291453960432414169609769428496000583489655320/456081057036098369813287"
    ],
    [
      "60056707550722616141348676651437904/255413572691007241",
      "-14289421860151373856301539991843333049216594825264165/129082080905330591578736539"
    ],
    [
      "3259434083547439700396308311/6652522969",
      "-184799626035881204338914001530255462840520/542599730920547"
    ],
    [
      "-53079669040417958915486886/824206681",
      "-92239542195603261459597999793285725115/23662149604829"
    ],
    [
      "30722454113649421246579138284424618640163931/92361271221104324356723689",
      "-167770006563695324352893199571176119972803728867667829490301785940/887635887434343098914013506069275300363"
    ],
    [
      "2271291652909427597718767275667199/30189726576151921",
      "-79361401802522867086726690423434051554227883439160/5245522685173883300071031"
    ],
    [
      "1335365901612724479084981/23697424",
      "-789236034633041293789844329354668145/115359060032"
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  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2old141516171819-022, rational kernel x=528240160300186247/4. Source: https://dujella.github.io/tors/z2old141516171819.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.",
  "created_at": "2026-09-26 20:43:32",
  "updated_at": "2026-09-26 20:43:32"
}