{
  "id": 432,
  "curve_key": "6452278965320791963061063078558361601:-16507270803116333505563169916983406268013689338374478849",
  "ainvs": [
    "1",
    "0",
    "0",
    "-134422478444183165897105480803299200",
    "19105637503606867472088832718752567503960757778399232"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "naive_height": 254.28679192051908,
  "faltings_height": 19.041091439209897,
  "conductor": "2021144615126579179797246594395487085729173432156567123503881134380779681747410",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "31",
    "47",
    "577",
    "1997",
    "4967",
    "13967",
    "577871576750005687906572281720218749111626260720627867331"
  ],
  "discriminant": "-2239196697651177772152759233975931016330047275115124817633287595245219412904559503368757740795534131200000",
  "regulator": "825016574380675822272.17032094673594973504181423338175769897752097977015566293471",
  "points": [
    [
      "613139836370682904",
      "-408888655747451285936040152"
    ],
    [
      "551746626861539392",
      "336011296136689273549138048"
    ],
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    ],
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      "-75967341146435456",
      "-169938063534571885141980032"
    ],
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      "410074257731562304",
      "-181496265704046836369274752"
    ],
    [
      "248811965003423104",
      "-32603939042290837423713152"
    ],
    [
      "21824084168107504",
      "-127210002083015654771879552"
    ],
    [
      "255785813086079104",
      "-38176104171018025013293952"
    ],
    [
      "267888791026421848",
      "48168888046161787573326016"
    ],
    [
      "-49502328603666656",
      "160120450656397462249948288"
    ],
    [
      "212349014807430784",
      "-11679919500181940888150912"
    ],
    [
      "268856937647001844",
      "48982554997139201244521788"
    ],
    [
      "304892167001311744",
      "80397878558931139243938688"
    ],
    [
      "22066522863279322984",
      "103643313473419608478135515328"
    ],
    [
      "-250731183859414976",
      "-192476092738925963056640192"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = 32/3. The 4 points beyond the seventeen generic sections came from searching the 1311 norm-4 quartic covers of the Mordell-Weil lattice; the claimed lower bound is rank >= 21.",
  "created_at": "2026-08-30 04:29:49",
  "updated_at": "2026-08-30 04:29:49"
}