{
  "id": 3112,
  "curve_key": "4934993511006419128829071018016411134927078180801:-10512727312657471988209043804746509244666320977394614305648076051717851201",
  "ainvs": [
    "1",
    "0",
    "0",
    "-102812364812633731850605646208675231977647462100",
    "12167508463723925912278977317426206869256513580773249167860386181829375"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "naive_height": 336.36130746511935,
  "faltings_height": 25.96005685928259,
  "conductor": "14131461780078584529422651011842782186617799735577501195",
  "bad_primes": [
    "3",
    "5",
    "7",
    "11",
    "29",
    "53",
    "103",
    "181",
    "193",
    "503",
    "641",
    "647",
    "1447",
    "1559",
    "2251",
    "2663",
    "7949",
    "14341",
    "298819",
    "23023237"
  ],
  "discriminant": "5596175186400419759349201674257872288522340353640313517014047871833701468620630841833224333851380824334001136257938515163216374679605388330625",
  "regulator": "35240276001065.4173206648436641456526049036452051012597899122",
  "points": [
    [
      "141257414375475714584782",
      "21519796839361935785539848033575341"
    ],
    [
      "199036391321563943854155442945/1721344",
      "96490065333677405391961299022603551642993775/2258403328"
    ],
    [
      "3641575186809420872229655",
      "-6923073843033886379901253772520558950"
    ],
    [
      "59376118330172978169143076313/9",
      "-14468306595445507319951979509322114685015868/27"
    ],
    [
      "25398274752370876794399209499347725/104662602256",
      "-1315068399433181334847839333306753772395150705715675/33860026431452096"
    ],
    [
      "1074843920241555035365071550/4489",
      "10750074646433837886643670986457295796375/300763"
    ],
    [
      "173453390832566308708898447650/452929",
      "51872071272199508638145544338786387805477775/304821217"
    ],
    [
      "493026883703641677487034060130706/364771801",
      "-10662489716302206755337357934797453122180508147227/6966776627299"
    ],
    [
      "4122161988761383787263285867120207/18730933321",
      "-36241316960588384732379720525449134731077010005813/2563534265245381"
    ],
    [
      "4244294530197556670751328090871010/185810137249",
      "7941497812805994987904523663716002524052240377135055/80094760332142193"
    ],
    [
      "209521965322266556645612688845/22801",
      "-95848030820950229732576733720455579267007200/3442951"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z4old9101112-012, rational kernel x=184273670355417640439200. 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 20:37:52",
  "updated_at": "2026-09-26 20:37:52"
}