{
  "id": 464,
  "curve_key": "1699277052694330243655821320148034059921:-69535601512375658277980310299699685297577007699173964685625",
  "ainvs": [
    "1",
    "0",
    "0",
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    "80481020268953308189156706852613645754737587637675825921"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 270.9930645727769,
  "faltings_height": 20.43451498852352,
  "conductor": "44513751878116744809773860414183449796086120374745760991466219808902636877123326",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "17",
    "29",
    "37",
    "43",
    "71",
    "83",
    "103",
    "6779",
    "9119567",
    "17853897615847",
    "62054470788771975296126013819524170351"
  ],
  "discriminant": "41397473566786685512109309127918766973738082017784807821951030869582035307344006094470887808377159726211356147712",
  "regulator": "114159273959719202761.126589089576499205211515498368367752389840490127554721944",
  "points": [
    [
      "4190823300449749966",
      "-2392190924489904348627874487"
    ],
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      "79482669854674265086/25",
      "-31835217305439196881434007931/125"
    ],
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      "-6628662597856198898",
      "4887575943667654893915617929"
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      "-12405576527360541106812564335"
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      "3833187437122701088",
      "1049906695094716923748723009"
    ],
    [
      "3699772208237333230",
      "-383132032305142354899113879"
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      "2967800786192471374",
      "1247408223725656108811532265"
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      "3029407129826290798",
      "-1018305369778353646698559511"
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    [
      "3672629762602663150",
      "35075899180128590712246889"
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    [
      "2996304785754007444",
      "1143404147540295320516402851"
    ],
    [
      "3191464387981609846",
      "-67398747914465660495932559"
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    [
      "2075600318202276010",
      "3992914407127106993376626209"
    ],
    [
      "1005525742642129438",
      "6774988105968135644141239753"
    ],
    [
      "4180199395378808518",
      "2353791745925512727859789049"
    ],
    [
      "719256274657338238",
      "-7442465055852688040358540791"
    ],
    [
      "784232354887054504",
      "-7293850484984624398670331929"
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  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = -41/35. 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 20:00:57",
  "updated_at": "2026-08-30 20:00:57"
}