{
  "id": 2832,
  "curve_key": "38478444952181142680005096861441:-272773653824278352602540030784120633156544005761",
  "ainvs": [
    "1",
    "0",
    "0",
    "-801634269837107139166772851280",
    "315710247481803582042676623278248394848262400"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    7
  ],
  "naive_height": 218.44994305829408,
  "faltings_height": 16.187604181865467,
  "conductor": "20846457077884763415090",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "37",
    "43",
    "1350840962771"
  ],
  "discriminant": "-10089489280052470282128853476634369888806694555528023132829052088414611416865430405120000000",
  "regulator": "15930.9011198473094061943555408856858658967184466",
  "points": [
    [
      "85526630898592",
      "15740863331343335618992"
    ],
    [
      "290385834223569760/961",
      "-299500046651904120799989680/29791"
    ],
    [
      "-178019446528040",
      "-21278513390150019041480"
    ],
    [
      "-81372900992864",
      "-19503915948192485780048"
    ],
    [
      "-437834763635540",
      "-24140442806878317303980"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Elkies (2006). Source: https://dujella.github.io/tors/z7old5.html (curve entry 2). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:24:25",
  "updated_at": "2026-09-26 20:24:25"
}