{
  "id": 4070,
  "curve_key": "21186980590808010627542883370273137811932537298479781081:-280040312928338501648986424144584957657278084152984934587639148793310027503769891485",
  "ainvs": [
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    "324120732555947339871512064945375563392437578948692835106747039439133358282465532"
  ],
  "rank_lower_bound": 20,
  "torsion": [
    2
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  "naive_height": 384.2886522001353,
  "faltings_height": 30.077189577623948,
  "conductor": "6131429525853961023265331906599034669054966945113256585858859273406727832034414573630186014",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "17",
    "19",
    "31",
    "47",
    "61",
    "71",
    "73",
    "97",
    "101",
    "151",
    "157",
    "163",
    "211",
    "317",
    "331",
    "337",
    "409",
    "431",
    "521",
    "541",
    "739",
    "761",
    "1637",
    "3433",
    "6397",
    "22037",
    "81157",
    "472859",
    "2737040129"
  ],
  "discriminant": "-39879625241025087593164194375504055816857517313087647708794127608108520772982930296251239372408049327177673981806841816425762139399640332231291042943185175321540828",
  "regulator": "7296121240460681268714.42200590872554833194799249069269740714802441728453892453",
  "points": [
    [
      "-896079305954870452843526387",
      "363159784079992967568442975956215233370"
    ],
    [
      "-43042296185941374974509729",
      "18521329960270726980163298379689831813280"
    ],
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      "-859021921477439840023600531",
      "8330712785955707958638570598619348409592"
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      "-895084829929099000762398259",
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      "407562830856814350456275105",
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      "15707337404075829720375904095998803903146"
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      "697504250391677475084683186",
      "18857090382173184954807834834874526061858"
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      "761772961032593099800988489",
      "20734825512184336678064182408318128828282"
    ],
    [
      "804480365436112376541599911",
      "22128654386237525219556254400035578288580"
    ],
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      "855296689130705625912900668",
      "23922247926985594246863085953409172793075"
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    [
      "-194557269099799315344472126",
      "20065715455933393230754053784577835250923"
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    [
      "-474628657528661224209280819",
      "20656692219121572724377928033741514984280"
    ],
    [
      "-518343353274041230288511590",
      "20338306574423649200623847257747390904331"
    ],
    [
      "-567289971995044886548302004",
      "19797875103834318364019451347863582692723"
    ],
    [
      "-775905464865785496290621732",
      "14123881960256940286524165863729095530800"
    ],
    [
      "1361844712068944471474046509",
      "47420612926951632727479946250310265232568"
    ],
    [
      "5559548004942856616393295613",
      "411956141695244294337953715631935347354120"
    ]
  ],
  "submitter": "wgxli",
  "history": [],
  "commentary": "specialization at T = -682893/97948 of the rank-9 fibration of X660 given by:\ny^2 + (4634T^2 + 5264T - 4032)xy = x(x + (43T - 5553)(93T - 193)(235T + 279))(x + (1 - 39T)(2220T - 961)(63T + 47)(T - 9)).",
  "created_at": "2026-10-09 03:51:12",
  "updated_at": "2026-10-09 03:51:12"
}