{
  "id": 3118,
  "curve_key": "70078579278752464923810091500380866465634113:-277333028571042489597906887979736099959660486443796247591419812065",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1459970401640676352579376906257934718034044",
    "320987301586854733330789085776409688960966170493687125337640464"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "naive_height": 302.8745732379711,
  "faltings_height": 23.292572946701892,
  "conductor": "5300423313342790652288129860235660003742350867406",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "29",
    "31",
    "41",
    "59",
    "61",
    "79",
    "163",
    "601",
    "607",
    "1231",
    "1327",
    "2652103",
    "4368649",
    "823091551"
  ],
  "discriminant": "154654400366966794418098748571230938665625480794206374985557209664330968501993800518362480955123419359380212703337968300489703424",
  "regulator": "9397427525292.03567514102025986377346817220489321033811411609",
  "points": [
    [
      "2867062906556364017179136376/744769",
      "146212873126244780502580002302709651500604/642735647"
    ],
    [
      "646728688219721393656164243594/586366225",
      "102817264565527037323299906645417597907083498/14198858138375"
    ],
    [
      "5480996156873503165116386424/95277121",
      "-14322909273385233997766737694284872369842748/929999978081"
    ],
    [
      "186719146294659345200877020071980/26863489",
      "-2551427740006342224885349948609991970048439339956/139233463487"
    ],
    [
      "42338629215192051833116629048/33953929",
      "-4146915051642691449535654394846912441142228/197849544283"
    ],
    [
      "285663722724101353664903955761269700664/1960476195880225",
      "4828005182116638655191130930366095643474961334920503440708/86804524051180630584625"
    ],
    [
      "8900241949697427913200280/6561",
      "-15373022865136613195758411448321048348/531441"
    ],
    [
      "777687582068898806019580399229489646/437697990240289",
      "-528904881948689787115700525780717579726481043738228686/9157181637448812156337"
    ],
    [
      "-388095910742608519409736970989649607437694/509874778343733999849",
      "-362485932827031028831874780675472761489082762924129327367255594/11513179992111684147547796549493"
    ],
    [
      "82021428715354816101559409804784401009106/53101966424431694449",
      "-16192413635241542316214493051244144812711126820189640717596048/386959849682067640134596471543"
    ],
    [
      "4977497474745332074646730135237383243185464/4427087761620405282025",
      "-2957076939130131937439112705697247261710021652513715012032609772/294562323674673506804521139915125"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z4old9101112-013, rational kernel x=653020238752531025784. 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 20:38:09",
  "updated_at": "2026-09-26 20:38:09"
}