{
  "id": 11,
  "curve_key": "963252595947625276081593994048250052044651054984589912081:-29792112590906400787516499632162945722111222184084598858916705933795305936274003718521",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-20067762415575526585033208209338542750930230312178956502",
    "34481611795030556467032985690390720374855944359319180361266008296291939448732243429"
  ],
  "rank_lower_bound": 28,
  "naive_height": 393.62973210050865,
  "faltings_height": 30.62346919240302,
  "conductor": "3455601108357547341532253864901605231198511505793733138900595189472144724781456635380154149870961231592352897621963802238155192936274322687070",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "48463",
    "20650099",
    "315574902691581877528345013999136728634663121",
    "376018840263193489397987439236873583997122096511452343225772113000611087671413"
  ],
  "discriminant": "3581775273581124569703746471783026864293570422220790957452423023734755536293093609524369063657264581131816964723217401534371110750621252297523717205467915359744000000",
  "regulator": "38572982340116091955788421590086427.57129683705100007574236938040229642098246623022300921177646",
  "points": [
    [
      "-2124150091254381073292137463",
      "259854492051899599030515511070780628911531"
    ],
    [
      "2334509866034701756884754537",
      "18872004195494469180868316552803627931531"
    ],
    [
      "-1671736054062369063879038663",
      "251709377261144287808506947241319126049131"
    ],
    [
      "2139130260139156666492982137",
      "36639509171439729202421459692941297527531"
    ],
    [
      "1534706764467120723885477337",
      "85429585346017694289021032862781072799531"
    ],
    [
      "-2731079487875677033341575063",
      "262521815484332191641284072623902143387531"
    ],
    [
      "2775726266844571649705458537",
      "12845755474014060248869487699082640369931"
    ],
    [
      "1494385729327188957541833817",
      "88486605527733405986116494514049233411451"
    ],
    [
      "1868438228620887358509065257",
      "59237403214437708712725140393059358589131"
    ],
    [
      "2008945108825743774866542537",
      "47690677880125552882151750781541424711531"
    ],
    [
      "2348360540918025169651632937",
      "17492930006200557857340332476448804363531"
    ],
    [
      "-1472084007090481174470008663",
      "246643450653503714199947441549759798469131"
    ],
    [
      "2924128607708061213363288937",
      "28350264431488878501488356474767375899531"
    ],
    [
      "5374993891066061893293934537",
      "286188908427263386451175031916479893731531"
    ],
    [
      "1709690768233354523334008557",
      "71898834974686089466159700529215980921631"
    ],
    [
      "2450954011353593144072595187",
      "4445228173532634357049262550610714736531"
    ],
    [
      "2969254709273559167464674937",
      "32766893075366270801333682543160469687531"
    ],
    [
      "2711914934941692601332882937",
      "2068436612778381698650413981506590613531"
    ],
    [
      "20078586077996854528778328937",
      "2779608541137806604656051725624624030091531"
    ],
    [
      "2158082450240734774317810697",
      "34994373401964026809969662241800901254731"
    ],
    [
      "2004645458247059022403224937",
      "48049329780704645522439866999888475467531"
    ],
    [
      "2975749450947996264947091337",
      "33398989826075322320208934410104857869131"
    ],
    [
      "-2102490467686285150147347863",
      "259576391459875789571677393171687203227531"
    ],
    [
      "311583179915063034902194537",
      "168104385229980603540109472915660153473931"
    ],
    [
      "2773931008341865231443771817",
      "12632162834649921002414116273769275813451"
    ],
    [
      "2156581188143768409363461387",
      "35125092964022908897004150516375178087331"
    ],
    [
      "3866330499872412508815659137",
      "121197755655944226293036926715025847322531"
    ],
    [
      "2230868289773576023778678737",
      "28558760030597485663387020600768640028531"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Found by Elkies (2006). A historical rank ≥ 28 record, via Dujella's elliptic-curve rank-records tables.",
  "created_at": "2026-05-27 22:11:54",
  "updated_at": "2026-07-02 01:49:25"
}