{
  "id": 3126,
  "curve_key": "4878473027774677915660490129112329809198838830801:-10775191282420916712022940045537467096034346179159807064896673488524486201",
  "ainvs": [
    "1",
    "0",
    "0",
    "-101634854745305789909593544356506871024975808975",
    "12471286206505690638915431397948987770853556352343302542131897789660000"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    4
  ],
  "naive_height": 336.32675019141,
  "faltings_height": 25.613483269002618,
  "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": "270356980638634919766539697028818833193340216949365998398398898998347077900500371667194279053453810888366979612519575115646868268687890625",
  "regulator": "17620138000532.7086603324218320728263024518226025506298949561",
  "points": [
    [
      "184273813157271150694825",
      "-5800120553079609944828465423975"
    ],
    [
      "13540059657277308942891228095200/64947481",
      "9703933638564341763425152122984447169226416600/523411749379"
    ],
    [
      "10439427866750933876145376/25",
      "25873516969122592126593637840797101384/125"
    ],
    [
      "96164102596179060057910300/529",
      "20443284097289870153353460052539737550/12167"
    ],
    [
      "147695786024769367617907",
      "26116833670524048667487732980486591"
    ],
    [
      "601720560802859926798220117431825/2476953361",
      "5672638138756500060760467950762479369890380352350/123275491823609"
    ],
    [
      "486520786037421216051947965020025/2637130609",
      "37385262874649760446614058889165133907848671425/135424568163977"
    ],
    [
      "62843966891152815754954481851598764/318758480569",
      "-1771182795506624093112488914428586373960777469699694/179966894269010003"
    ],
    [
      "1843846985114411609283367250604129989425/10030607985443929",
      "79753941216730576626745820381367024922370814619338633050/1004594709209350941954467"
    ],
    [
      "10450311344654113796382091700219599/23850169225",
      "-840415618470099135217423352461674911178511257497327/3683300884262875"
    ],
    [
      "1578053822431536957304631565513264818537200/3361290514949472121",
      "-1609750667644382187352038513122797303530701995993489381708885100/6162530404175917497955445581"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2z2old1011121314-049, rational kernel x=-1474189362843341123513601/4. Source: https://dujella.github.io/tors/z2z2old1011121314.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 20:38:31",
  "updated_at": "2026-09-26 20:38:31"
}