{
  "id": 629,
  "curve_key": "9895030694214226323552866859539205819046957275040081:-954989066308591641010061865335632819629565930947042022971753565174973709040729",
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  "rank_lower_bound": 27,
  "torsion": [],
  "naive_height": 359.17161727121515,
  "faltings_height": 27.84558457943541,
  "conductor": "1501492496847230651915535798135038791367857964464751861873735344250891303798770296273960611057947540201444218392271650661570",
  "bad_primes": [
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  "regulator": "35972256687617507862791281178743.974666367850133064664882815135281207363181440640813284688707",
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      "-5572228242459733050532278409188498850651011129563/4195872914689"
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      "25693823873572829308390503981657886/6799156849",
      "10932525244415905436238563886337946791227021141089789/560638076297993"
    ],
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      "1734020861094651845518161190342579621/490576969744",
      "-7048663114128752511391337731329465183281718782416118551/343605996532334528"
    ],
    [
      "-4919666575019428834163612991825374/1207354009",
      "1817855779352831733737175913384877974261678062951799/41951929750723"
    ]
  ],
  "submitter": "Roy van Rijn",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Roy van Rijn",
      "at": "2026-09-07 08:41:48"
    }
  ],
  "commentary": "This curve was found prospectively as the specialization t = 3726/881 of an elliptic K3 family with generic Mordell–Weil rank 17.\r\n\r\nWe found 27 independent rational points on the specialized curve, proving rank at least 27 over Q; the exact rank is not currently known. The submitted equation is a globally minimal integral Weierstrass model. In this presentation, the specialization has 10 independent directions beyond the 17 generic sections.",
  "created_at": "2026-09-07 08:27:41",
  "updated_at": "2026-09-07 08:41:48"
}