{
  "id": 3194,
  "curve_key": "413780312755197706622041701649:-266106751962265183649740033393400779605572857",
  "ainvs": [
    "1",
    "0",
    "0",
    "-8620423182399952221292535451",
    "307993925882250651596378357172269498313681"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2
  ],
  "naive_height": 204.58539809491063,
  "faltings_height": 14.770842828879985,
  "conductor": "37047639080308908544920171799389911308078271310",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "29",
    "109",
    "113",
    "157",
    "173",
    "541",
    "827",
    "2083",
    "4231",
    "5171",
    "14177",
    "1708781"
  ],
  "discriminant": "18657376427921023421562941463757361799811320362964128307693739144084575894896640000",
  "regulator": "1821088857816859.24352758318231258467301407176464633221833703086490",
  "points": [
    [
      "29093173328111017326/534361",
      "2589793618487742939741679347/390617891"
    ],
    [
      "2897923327950033486/44521",
      "1414172828802726748508404827/9393931"
    ],
    [
      "4957470356280809506/77841",
      "2856686448349795537666708163/21717639"
    ],
    [
      "3365457178734911624286/829921",
      "195188056946779226073953255873727/756058031"
    ],
    [
      "329859401341993576014/223729",
      "5979314538835318941954862494489/105823817"
    ],
    [
      "95750181892299249474/966289",
      "620512883011027916764823306979/949862087"
    ],
    [
      "-1264828292670667338725769762/119250964603681",
      "821790920259739013574046578569633316149025/1302245456923798689329"
    ],
    [
      "5359430132780313/256",
      "1514404970292049978539675/4096"
    ],
    [
      "8772248890687182/169",
      "43312652419056610859589/2197"
    ],
    [
      "11306018566339271922371834334/238943797249249",
      "287052924139605892576319097109903152538431/3693547101726021936943"
    ],
    [
      "-217190686146220834/2209",
      "47018791854231809432911519/103823"
    ],
    [
      "108059385100640211534/1974025",
      "-32679481753615930720539642987/2773505125"
    ],
    [
      "97699884711223398068876287716606/12254654943555025",
      "-965632242633271672550174172878308007990557511031/1356599431969474215993625"
    ],
    [
      "1356594417467846/25",
      "-15734186252882024771/125"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2old141516171819-072, rational kernel x=-423545465356529/4. 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 20:42:04",
  "updated_at": "2026-09-26 20:42:04"
}