{
  "id": 4072,
  "curve_key": "41648478512520856485725068104729336579755268634123975425:-268780423466083194112850649733974015161115047674316478281129941320069430251192170625",
  "ainvs": [
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    "-1",
    "1",
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    "311088453085744437630614178149759454244744099375091764759736060102972383223090347"
  ],
  "rank_lower_bound": 20,
  "torsion": [
    2
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  "naive_height": 384.20657957793736,
  "faltings_height": 29.60875697844481,
  "conductor": "6298072849453555625678659198919335015893455426961399018547798525692978105732842174850",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "19",
    "23",
    "29",
    "41",
    "43",
    "67",
    "73",
    "83",
    "89",
    "109",
    "139",
    "173",
    "181",
    "919",
    "1217",
    "1931",
    "2459",
    "2719",
    "3533",
    "4259",
    "4993",
    "8081",
    "9629",
    "100547",
    "234673",
    "761667509"
  ],
  "discriminant": "207349507308655959429075239992235161493301950303762984422555754646003655731912246841381845272444622717259713761380871975356918479806824623048813922750464000000",
  "regulator": "6614713888757303096074.12946211246860621191527943551907107372093927786575789135",
  "points": [
    [
      "537103011622895827301431819",
      "2262879917470743071106446787409366490"
    ],
    [
      "537103128729420844962838859",
      "2204222833813179042510783877422460570"
    ],
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      "536356417084628017197580993",
      "50729759566961893004743480179178214246"
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      "536573605711769480061355309",
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      "536855144983401242057788363",
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      "536869994860979884698992519",
      "24779399027036577462368337784618683790"
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      "538614744165844130634110659",
      "17554267866789550587294636082525913570"
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      "539022616076533063605727819",
      "40671574362993856732208035581949486490"
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      "522520521472896609741116059",
      "610064503056977981593492440499497318170"
    ],
    [
      "526187767614964180780636879",
      "463794314862434606644991859132030248810"
    ],
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      "533995395734437454642213579",
      "149966261911684362906877564477398960410"
    ],
    [
      "534472258814357217051407809",
      "130481396927432013832312323134367335270"
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    [
      "548944778074162872374777059",
      "448460772977082916517595712994736078170"
    ],
    [
      "551391844982372645913465019",
      "547659148376721415690757560730867153690"
    ],
    [
      "395576813832973677423270019",
      "5454901988140914932642746803559810118690"
    ],
    [
      "-492354403991238515008430621",
      "24878501303843316830319622042863486782810"
    ],
    [
      "9149673582550012756517405179",
      "870833521938189470864755667965125484684010"
    ],
    [
      "1435779919386465755736295915/4",
      "54192126177637093464498019511548432930969/8"
    ]
  ],
  "submitter": "wgxli",
  "history": [],
  "commentary": "specialization at T = 60273/42619 of the rank-9 fibration of X808 given by:\ny^2 + (367T^2 + 35464T + 23700)xy = x(x + (51T - 727)(635T - 429)(6T + 13)(55T + 59))(x + (13T - 25)(2548T - 55)(375 - 272T)).",
  "created_at": "2026-10-09 04:23:58",
  "updated_at": "2026-10-09 04:23:58"
}