{
  "id": 418,
  "curve_key": "39123510805641636202339429040616944368312300872063361:-8768506454954741080182147511210370650261444129613120198915542709137061536472641",
  "ainvs": [
    "1",
    "0",
    "0",
    "-815073141784200754215404771679519674339839601501320",
    "10148734322864283657618226218200352363193275261694417405081164533181261838400"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "naive_height": 363.5456074876304,
  "faltings_height": 28.275880242219493,
  "conductor": "78215928850816814315475228669912320288965457568304335441059486388743780155523303370660512822073067247701057863810237592566930",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "41",
    "43",
    "97",
    "100291",
    "12035614027",
    "136275301181889479",
    "53605277496717250253987332261938249194470530456940125692776944124494415356042639083"
  ],
  "discriminant": "-9839316513169517755920678269709069435748137552838716848014248656337848459529179209312843801536495603592215241976105162110825387465187436111452309913600000",
  "regulator": "110433344918437932892855708.09282462382429890159132163575510608127887573793464860",
  "points": [
    [
      "-24193508905300590986569520",
      "125328077111701337398503316998977565880"
    ],
    [
      "7316967155555376927038840",
      "-67650622789190337967249127905264805320"
    ],
    [
      "3030145243092182573283672928/9",
      "166221156943769535222386584652895806113592/27"
    ],
    [
      "-8058481787692539451029488",
      "-127254373620120059944647124767302342024"
    ],
    [
      "-133356623944165889347670240/9",
      "3719024356874097977774728808420741459960/27"
    ],
    [
      "-27436290212495229969200560",
      "108897426792187636691528695100525255480"
    ],
    [
      "22142803730800206405428240",
      "54382254266982487233889894163537615480"
    ],
    [
      "-21847915482072618180692440",
      "-132392171648216317435693360703937850720"
    ],
    [
      "22553058957892040455821206600",
      "-3386942588678979413347388688249237671751880"
    ],
    [
      "1249624670206398066102169840",
      "44162855241023436099699754654966659158680"
    ],
    [
      "263016412784901712238823440",
      "-4241535582865718771892073686401684304520"
    ],
    [
      "18414303912818040397247360",
      "37199103134317927234953814129256330360"
    ],
    [
      "519845112470884862648459210",
      "-11835067790366097054330785169242821864990"
    ],
    [
      "56398976758383860961014435/4",
      "-305625125424316624299280857866033500085/8"
    ],
    [
      "-11109213354771312142122310",
      "133538445381408206562089552031786490580"
    ],
    [
      "17533735018800278430757940",
      "-35325439395682660875327399924999823420"
    ],
    [
      "93836663343319906442405840",
      "-871737793894317089847017629827291048520"
    ],
    [
      "5953436900739983749707097640",
      "-459353097505040201928408381215711492103520"
    ],
    [
      "25925459376412850961181940",
      "-80267386214363440535026830312203324920"
    ],
    [
      "446770149468456587157768422373129560/14641242001",
      "-207287550354291895707005818896537906916774914194915720/1771604923363001"
    ],
    [
      "182709864693850184548404331808/5929",
      "-54585252132977821641470049096720287073551912/456533"
    ]
  ],
  "submitter": "7fff-zip",
  "history": [],
  "commentary": "Found in this search on Noam D. Elkies's published q1/q2 rank-19 pullback at t=-5440/1843 (u=849006/1843, v=10523171/1843).",
  "created_at": "2026-08-29 12:46:00",
  "updated_at": "2026-08-29 12:46:00"
}