{
  "id": 3188,
  "curve_key": "18899718284153408687858937841:-4279147153978146568287832574876631690600265",
  "ainvs": [
    "1",
    "0",
    "0",
    "-393744130919862680997061205",
    "4952716613400599790174081417550462849761"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2
  ],
  "naive_height": 196.32465526479777,
  "faltings_height": 14.396650640877175,
  "conductor": "300953424448851386334317567807295829194402996102",
  "bad_primes": [
    "2",
    "3",
    "23",
    "29",
    "71",
    "73",
    "101",
    "257",
    "307",
    "353",
    "449",
    "1181",
    "3511",
    "4217",
    "16561",
    "204751"
  ],
  "discriminant": "-6689891930585676000307597032645591964221040103265199283004176232615267149826490368",
  "regulator": "358410078857257.841950288637918180941690802449631611601764979796683",
  "points": [
    [
      "-6372209542377614/361",
      "-548852388221684244189251/6859"
    ],
    [
      "107675046974519266/15625",
      "98948474849875970557117811/1953125"
    ],
    [
      "-1627690600873586366/85849",
      "1882735939282522808454741947/25153757"
    ],
    [
      "-639563558500833998/117649",
      "-3359916083270508286819461887/40353607"
    ],
    [
      "7857406760540602882/11449",
      "22016109232939843856176493717/1225043"
    ],
    [
      "-8022914243186",
      "-87150898802595089729"
    ],
    [
      "1602997543139990818/72361",
      "1640340770295025500677903747/19465109"
    ],
    [
      "872227104966370/169",
      "-121493063200393358730173/2197"
    ],
    [
      "8847379658179771410340/576816289",
      "-695696047182503994718169165634793/13853396812913"
    ],
    [
      "1540298477232754/49",
      "-52734276279490976627087/343"
    ],
    [
      "3487630933315490662/1338649",
      "-97274644568460341566690379281/1548816893"
    ],
    [
      "2297186214097913026/151321",
      "-2927794232721542010368260453/58863869"
    ],
    [
      "8400705059447479090/22201",
      "-24316191262061460024867995749/3307949"
    ],
    [
      "1039385118855579298/100489",
      "-1419844613583190835327695693/31855013"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2old141516171819-054, rational kernel x=195391032383343/4. 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 20:41:46",
  "updated_at": "2026-09-26 20:41:46"
}