{
  "id": 2921,
  "curve_key": "-2430100875152073946971817199:-27268597267340397811539800704512294814201",
  "ainvs": [
    "1",
    "0",
    "0",
    "50627101565668207228579525",
    "31560876466833383058857093536380500625"
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  "rank_lower_bound": 7,
  "torsion": [
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  "naive_height": 189.173190839215,
  "faltings_height": 13.83662323871519,
  "conductor": "98401480189946941347452490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "19",
    "23",
    "31",
    "53",
    "73",
    "167",
    "4139",
    "16691",
    "774901"
  ],
  "discriminant": "-8735110210745040575633189159338404212814641711059404452828409934970703062400000",
  "regulator": "983427.3277015715089767112757879686903438280297491906",
  "points": [
    [
      "-605169073250",
      "-837429992429581775"
    ],
    [
      "-364576031330",
      "-3613168901523318095"
    ],
    [
      "-235888035350",
      "-4427801072954045975"
    ],
    [
      "1546697018650",
      "10656724003864614025"
    ],
    [
      "-574263218390",
      "-1515986080954691735"
    ],
    [
      "3969736276270",
      "17178339680519480305"
    ],
    [
      "-367692673010",
      "-3591093088057271375"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Lecacheux (2009). Source: https://dujella.github.io/tors/z5old678.html (curve entry 28). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:28:29",
  "updated_at": "2026-09-26 20:28:29"
}