{
  "id": 3131,
  "curve_key": "5279330611395457723474507892963226688:-12128089578084679263174477018189191283497402498529149440",
  "ainvs": [
    "0",
    "1",
    "0",
    "-109986054404072035905718914436733889",
    "14037140715375786147567700636361626091030503635127071"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "naive_height": 253.67058797796597,
  "faltings_height": 18.852635414025144,
  "conductor": "725195062080830777445016962580423655128128",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "29",
    "41",
    "47",
    "53",
    "61",
    "89",
    "193",
    "233",
    "257",
    "419",
    "509",
    "683",
    "3037",
    "14519",
    "22129"
  ],
  "discriminant": "29755690648100452225526027887626920749885367041422075731236756304863192205631185820219558357449795764224",
  "regulator": "37045299241.3464967059622169889809935468565471457906322268206",
  "points": [
    [
      "282833611654981348917/1444",
      "-162095409908071355030171542335/54872"
    ],
    [
      "1564244656360110333099/1225",
      "-59959307884135903804547856868032/42875"
    ],
    [
      "1960618722959114340708285/315844",
      "2741459360360983225512801659236964043/177504328"
    ],
    [
      "11498584646133551250192381768942237/41474909763286609",
      "-588479138380477376774947257776255411687389283945100/8446527001016665450765273"
    ],
    [
      "7187166168051981812387706/34586161",
      "-2533212697157206573214182294398838257/203401212841"
    ],
    [
      "21578424639246648404981552297205882/74238869332163449",
      "-1646391459037175390322535218214909771374499485091485/20227724192754929163621043"
    ],
    [
      "5355894392417124758385687915/13756681",
      "-391965506315543101726749612068306713324224/51023529829"
    ],
    [
      "1010044240733075184289216341724212242068329/274625795236906728388225",
      "-1011112625990006542457516111782877687521439398114444339744958208/143916964830653352754118171775666625"
    ],
    [
      "3104791397761565669248264573165136338903667314128059124563351016415381174458/16031910610981581591445839763999664152590635106471451798081",
      "-1133986151981100864247500998038710363029211067262316237778115669614980171655742646753586101656382512423191295385/2029915333088671562483843803605153471562221042837965597899940564791293287865332867226271"
    ],
    [
      "749503108008605084181/3721",
      "-1689798906465476276023816928172/226981"
    ],
    [
      "194929629094072269",
      "-2109564027247788109727820"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z4old9101112-014, rational kernel x=-378805909904245639. 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 20:38:43",
  "updated_at": "2026-09-26 20:38:43"
}