{
  "id": 67,
  "curve_key": "2672215049531731291973653104974237283828192744046561:-139952357558889314302863352224099518925635263844664742670201709209325962815825",
  "ainvs": [
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    "-55671146865244401916117773020296610079754015500970",
    "161981895322788558220906653027519611838007321625214218991719656790551905956"
  ],
  "rank_lower_bound": 27,
  "naive_height": 355.2703680721914,
  "faltings_height": 27.482287272229936,
  "conductor": "44473459337320533154136751324343533168070733706606064610068741773097621300831711931623980390498751106487256208641524555812214",
  "bad_primes": [
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    "3",
    "7",
    "13",
    "19",
    "23",
    "29",
    "43",
    "97",
    "1333872817",
    "622918016143240238107",
    "4018426744559269274579405699",
    "461516545359925528236128783904359556661401233959492820033"
  ],
  "discriminant": "-292295992467036730780372591065803086322380999542983847983425194363595329691796423905092278238635719085287829796511182852120658943291432879857572200448",
  "regulator": "70127565624872862829955299377887.957802713297922693486537158452665203606944461202704437006234",
  "points": [
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      "-4503215618194252049902522",
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      "26398450763063898266637186797421380678"
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      "8894515448962144734398280820434671978"
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    [
      "4667249764662401626929236",
      "1954092716090144351072720616414325286"
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    [
      "3131745787384349113625300",
      "4283649283716227803355987840842617734"
    ],
    [
      "243907731994687263474127628",
      "3807478665185691587984635270031859346574"
    ],
    [
      "110171466072672245507182388",
      "1153803508275547153736593941741941166854"
    ],
    [
      "2631452133741740392491152",
      "5805818938673165314161211507146370634"
    ],
    [
      "2398961346477899287733092916",
      "117498623151243646059583140149253976390406"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Provenance: Andrej Dujella rank-record table \"Rank >= 27\", Elkies (2016). The page lists this curve y^2 + xy = x^3 - 55671146865244401916117773020296610079754015500970*x + 161981895322788558220906653027519611838007321625214218991719656790551905956 and the 27 independent points submitted here.",
  "created_at": "2026-05-29 04:46:51",
  "updated_at": "2026-07-02 01:49:26"
}