{
  "id": 3080,
  "curve_key": "0:-75427041968543257139493897140033496",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "87299817093221362429969788356520"
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  "rank_lower_bound": 9,
  "torsion": [
    3
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  "naive_height": 160.61694785263336,
  "faltings_height": 11.442401563511076,
  "conductor": "9428380246067907142436737142504187",
  "bad_primes": [
    "3",
    "13",
    "23",
    "31",
    "43",
    "61",
    "73",
    "157",
    "199",
    "337"
  ],
  "discriminant": "-3292383483868278860615936775487253728617635387261104834928937501147",
  "regulator": "736237929.26318997057405429927313082439417920105472609687",
  "points": [
    [
      "-34739896854",
      "6735993625205487"
    ],
    [
      "59816792760",
      "17358779174601879"
    ],
    [
      "-44207258970",
      "952038792981504"
    ],
    [
      "6576595440",
      "9358646559113879"
    ],
    [
      "55473407808",
      "16062629859888488"
    ],
    [
      "-19255568904",
      "8953228261141352"
    ],
    [
      "101583478425/4",
      "81458264395412407/8"
    ],
    [
      "11986370039488/81",
      "42053694778844172287/729"
    ],
    [
      "-2123513196948/49",
      "833762857240311704/343"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Elkies - Rogers (2004). Source: https://dujella.github.io/tors/z3old891011121314.html (curve entry 51). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:36:19",
  "updated_at": "2026-09-26 20:36:19"
}