{
  "id": 3200,
  "curve_key": "-14210960716437914114273133113941306079:-4748061821745835333226872569724192035650396842220396785969",
  "ainvs": [
    "1",
    "0",
    "0",
    "296061681592456544047356939873777210",
    "5495441923316939043111329873609778827340053867929755492"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
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  "naive_height": 265.61017359582,
  "faltings_height": 20.191893806912137,
  "conductor": "23693473551183573088015644406641907435184135279878499727924510",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "19",
    "37",
    "41",
    "79",
    "113",
    "193",
    "233",
    "241",
    "251",
    "269",
    "479",
    "727",
    "751",
    "853",
    "1153",
    "1291",
    "1373",
    "2273",
    "7283"
  ],
  "discriminant": "-13048009830206096170282046578924495340327005218624863678705108520539536411898146062737907277503381504000000000000",
  "regulator": "159564718935910448.85798915472698949688920696463176279611406120327048",
  "points": [
    [
      "-1707441811914673476",
      "110138399920174438467661338"
    ],
    [
      "16214483994960393324",
      "65370005857555056679736680938"
    ],
    [
      "746315197099198400016/2809",
      "352082505364800255629069394125826/148877"
    ],
    [
      "270182225276440575355404/44521",
      "142710829757887895214822369574564878/9393931"
    ],
    [
      "655266542151083753126124/22801",
      "530585124406304125119553064039617638/3442951"
    ],
    [
      "806131693786103131356/1369",
      "122763837782268842987429873616114/50653"
    ],
    [
      "-91964458657777773429684/162409",
      "148477221703908170356903721021970126/65450827"
    ],
    [
      "-450086322360134645610516/271441",
      "94405134443694043691118236118179418/141420761"
    ],
    [
      "-143200686165823869867396/96721",
      "-40487490236630616737121802218071322/30080231"
    ],
    [
      "-873226809807839466175628226/649689121",
      "-27056237418925394812010522599894825697388/16559926005169"
    ],
    [
      "113017516280882017992466524/446096641",
      "-22270064594626083497848273244898091008342/9422007154561"
    ],
    [
      "108609196040183374863262083217804/11812893386121",
      "-1137846794915182729008350482440717927750337580078/40600784626270629669"
    ],
    [
      "2366505932682481383669013284/3500641",
      "-115122852213689253049917786882231239216682/6549699311"
    ],
    [
      "1118526413682583359380556/5583769",
      "-31119840120239262416673972767628958914/13194446147"
    ],
    [
      "-305168440765452622608957700021743834/178800301712535409",
      "-10236535032977454682528258066515356519201738413121676/75605322622096010606914423"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2old141516171819-031, rational kernel x=13670258741780008607/4. 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 20:42:22",
  "updated_at": "2026-09-26 20:42:22"
}