{
  "id": 448,
  "curve_key": "3575712298420067147111745657674566081:-6727933244424466211342974013286344514902023562188141729",
  "ainvs": [
    "1",
    "0",
    "0",
    "-74494006217084732231494701201553460",
    "7786959773639428479142830515805837724808339207958672"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 252.50168324519524,
  "faltings_height": 18.87737407437709,
  "conductor": "5597199175118491536130878384121905070868151610189056358131211447741842709470",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "29",
    "79",
    "293",
    "4969",
    "577873",
    "1112129",
    "2081801",
    "161195362687",
    "127704680002349",
    "1312838632356181391"
  ],
  "discriminant": "262132484055168836760776897065169957848979652219168298752992435420665593103233127060118979791769600000000",
  "regulator": "80585923170408260509.4439505519871773282866932461825816391224276517472502299023",
  "points": [
    [
      "143328833763702184",
      "7365264967233225868986508"
    ],
    [
      "211681681290884584",
      "38771331505503406340173708"
    ],
    [
      "-86849014521118616",
      "116625941763599983922068108"
    ],
    [
      "657367978305645256/9",
      "1412160022537238039002482116/27"
    ],
    [
      "167340752077110664",
      "-2666020289432732823067412"
    ],
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      "166859614356416488",
      "1626606739477569271567756"
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      "146786267817812584",
      "-3866541915392189845714292"
    ],
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      "201469143426337384",
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      "288825516815339584",
      "101808969441344612700406708"
    ],
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      "147038410111124584",
      "-3534572130368119203538292"
    ],
    [
      "141549522230976184",
      "-8859618583682490364661492"
    ],
    [
      "-232174088258307416",
      "112103694389737149237781708"
    ],
    [
      "115652613551838184",
      "-26803878850670191783685492"
    ],
    [
      "148249760095449064",
      "-1213742693743867010801012"
    ],
    [
      "3672680386953849256/9",
      "5749342101630028560377298116/27"
    ],
    [
      "148336470899111638",
      "856894609833524368413736"
    ],
    [
      "77117944020970552936/529",
      "-61205693163657289604259710764/12167"
    ],
    [
      "204702475690244584",
      "-33399420957627968352466292"
    ],
    [
      "169353449692868584",
      "5319760375436060031757708"
    ],
    [
      "13678960832728296664/121",
      "-37886821218558886232409012652/1331"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = 5/16. The 3 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 >= 20.",
  "created_at": "2026-08-30 15:55:01",
  "updated_at": "2026-08-30 15:55:01"
}