{
  "id": 3582,
  "curve_key": "209787657467927652457786577132360007851025:51504090478261491804175842032331394971285778096053241986726375",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-4370576197248492759537220356924166830230",
    "-59611215831321171068555321265886250619474234373793543925228"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2,
    2
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  "naive_height": 285.44074347302586,
  "faltings_height": 21.83466285236148,
  "conductor": "519230428950677293578730527990684406193342087025",
  "bad_primes": [
    "3",
    "5",
    "7",
    "13",
    "19",
    "31",
    "37",
    "43",
    "47",
    "53",
    "79",
    "109",
    "113",
    "137",
    "167",
    "179",
    "263",
    "337",
    "823",
    "1171",
    "1471",
    "3461",
    "6269"
  ],
  "discriminant": "3808023231325566756786691244066517471249300112623658597991978332128576065559731252113668556287333611405080041563797265625",
  "regulator": "46474535308944672.175425713131857189068791080687541855985334274",
  "points": [
    [
      "-400438207751884348564580515/25684624",
      "-8960990825119638971794189623041990377923/130169674432"
    ],
    [
      "10303912351188598634891/4",
      "-1045585145936016434232217374727395/8"
    ],
    [
      "412704018312123506379",
      "-8272259911532268421961425218190"
    ],
    [
      "197951657429688072893381459/1999396",
      "-1954913971570042585175222857906851754485/2827145944"
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      "140640008884047141467397761196911163057400599247540/3830076040030719388209"
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    [
      "-2369442066995301837162024853025/41981551236",
      "733704347709681193042436039774771555582660297/8601767958948984"
    ],
    [
      "6944718771074236772885890021/95648400",
      "-71359439788984114913582995610867979553721/935441352000"
    ],
    [
      "45238516981088592060651/625",
      "-891302751775308498569492246112474/15625"
    ],
    [
      "5078562337614607619727592559/1452025",
      "361853921198510509651214366869735640106192/1749690125"
    ],
    [
      "-5775134324264871998796387239689/328877016484",
      "-20419764708047755793331227773490059191830449755/188603733659211352"
    ],
    [
      "-30976141141425795358834442483941/553961649796",
      "-41105845566151974971328462986096864786794106265/412305900480065656"
    ],
    [
      "87074803433113309987476353799/274200481",
      "25106987041393043679289385969561557815072240/4540485764879"
    ]
  ],
  "submitter": "Matej Jurasić",
  "history": [],
  "commentary": "2-isogenous to curve#3562, the fibre at t = 83497/251378 of the Z/4 fibration E1 of X163 from Elkies–Klagsbrun (arXiv:2003.00077, Sec. 9), who list this t among their rank-12 parameters.",
  "created_at": "2026-09-28 21:02:27",
  "updated_at": "2026-09-28 21:02:27"
}