{
  "id": 2784,
  "curve_key": "119730562380204344635215044911558622316241:-41429170493441491653369474309006591584531121614934274793271961",
  "ainvs": [
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    "47950428811853578302303100075736441050437846119869139884025"
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  "rank_lower_bound": 4,
  "torsion": [
    10
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  "naive_height": 283.7581875946668,
  "faltings_height": 21.24278200584295,
  "conductor": "17569174278352986897510210",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "23",
    "61",
    "79",
    "149",
    "181",
    "709",
    "10711",
    "19709"
  ],
  "discriminant": "5927243673102551071320762927517904179868335548961534601463645581140722578038457773804898582224376194417710000000000",
  "regulator": "179087.4451211278996846883999466263160349637546",
  "points": [
    [
      "28509015942778302410",
      "3003281534671521511510019045"
    ],
    [
      "-4710087341394312480646/289",
      "1426248104611211485908211687075441/4913"
    ],
    [
      "651746601062048885608610/27889",
      "229159071225334021088598309104574895/4657463"
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    [
      "2474363018938566848121587468060/27532433041",
      "3386940458446040733191786369680733084310244255/4568429082060089"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Elkies (2006). Source: https://dujella.github.io/tors/z10.html (curve entry 3). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:22:17",
  "updated_at": "2026-09-26 20:22:17"
}