{
  "id": 3085,
  "curve_key": "321234614816495470932694797287344:3023023405471396943735665892074996078102047811328",
  "ainvs": [
    "0",
    "1",
    "0",
    "-6692387808676988977764474943486",
    "-3498869682258563508267771748897941752628277240"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2,
    2
  ],
  "naive_height": 224.54917359978646,
  "faltings_height": 16.761322618181996,
  "conductor": "734580525126326665789875840301734560160",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "29",
    "31",
    "37",
    "41",
    "43",
    "163",
    "199",
    "229",
    "313",
    "1531",
    "18541",
    "53173"
  ],
  "discriminant": "13894715478174642653334291858041720100534300308598766793298204538999900808579987262355881960000",
  "regulator": "3119618200.250326330542250799162208189448449411595457314255",
  "points": [
    [
      "-568634665484218",
      "11081002979887647935700"
    ],
    [
      "-15825575908682863/16",
      "-2969565728584437386150175/64"
    ],
    [
      "-166008412224986299/196",
      "108443708345701496526295041/2744"
    ],
    [
      "-91060078215418579/100",
      "-42897078946186349308521669/1000"
    ],
    [
      "-19554463788667306/25",
      "4432185394671500279504028/125"
    ],
    [
      "1705570539314576966",
      "-2227429816741713780114063444"
    ],
    [
      "-4175562463625947/4",
      "387790920387792066063375/8"
    ],
    [
      "947318146534941175478512017495677/154311956729267236",
      "-26197572499128993356363772657875602671668921016675/60617687915220179917645016"
    ],
    [
      "69937837990825890665/21904",
      "-284170090010106145902351934275/3241792"
    ],
    [
      "11995192851768521",
      "-1281463535056311742707234"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z4old9101112-031, rational kernel x=4539034041928485. Source: https://dujella.github.io/tors/z4old9101112.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 20:36:33",
  "updated_at": "2026-09-26 20:36:33"
}