{
  "id": 434,
  "curve_key": "5747935663314913303367773817456213521:-13712510762858379065673606803640602091032755435521538681",
  "ainvs": [
    "1",
    "0",
    "0",
    "-119748659652394027153495287863671115",
    "15870961531086086871587619570217861268496637395066225"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "naive_height": 253.92571236917368,
  "faltings_height": 18.99582777367641,
  "conductor": "8326559330120298582074074068589703981740465847850520002266773544829744538239330",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "23",
    "29",
    "36353",
    "651943",
    "859287078407",
    "171533634337430750969577639730984194402389843219"
  ],
  "discriminant": "1083183267000326135418099570935273303254315599120654386377035262770393261696249926038970689754716416000000",
  "regulator": "735004338681961160047.70581984974834515047498418730602798814733316858827995015145",
  "points": [
    [
      "232947900586241110",
      "24831759567696378492034705"
    ],
    [
      "185846676119451430",
      "5918369614431624233449585"
    ],
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      "-1500955330983244280/9",
      "4769403201808716117844741045/27"
    ],
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      "216572043063620530",
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    ],
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    ],
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    ],
    [
      "1484016079930725646",
      "-1762502813953854779714571743"
    ],
    [
      "314609954198946130",
      "-96626875443399893613847415"
    ],
    [
      "-26216775763099298",
      "-137812793269428734988273503"
    ],
    [
      "-68822984830286690",
      "-154228514011438618725242495"
    ],
    [
      "666725929447237930",
      "-482085828257917450652365415"
    ],
    [
      "2270388951390146575/4",
      "2892891580565805360604773905/8"
    ],
    [
      "218347494902512630",
      "-11575652813224572493162415"
    ],
    [
      "-314101840271809320",
      "149983195871484412405438335"
    ],
    [
      "302863134182143870",
      "-85929940440540858266529215"
    ],
    [
      "-2019794321406410",
      "-126936286985641471736314415"
    ],
    [
      "3042688505153830",
      "-124525627203002953018006415"
    ],
    [
      "-4954306966644920",
      "128312554125616002986852335"
    ],
    [
      "-60601407603527090/9",
      "-3486763588060286085645067525/27"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [
    {
      "kind": "rank_improved",
      "user": "Jason Ma",
      "old_rank": 20,
      "new_rank": 21,
      "at": "2026-09-03 16:31:26"
    }
  ],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = 6/11. 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 04:29:51",
  "updated_at": "2026-09-03 16:31:26"
}