{
  "id": 2830,
  "curve_key": "6240369436106078609578908020406241:-531491113359644631701332172117967565661572674174289",
  "ainvs": [
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  "rank_lower_bound": 5,
  "torsion": [
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  "naive_height": 233.599541882862,
  "faltings_height": 17.423411597564048,
  "conductor": "2041902909193371038430",
  "bad_primes": [
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    "11",
    "23",
    "37",
    "67",
    "89",
    "137",
    "229",
    "521",
    "10657"
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  "discriminant": "-22840869305144453897277759214833559452196613288612279476258110366393029342795283787475192868000000",
  "regulator": "295271.154788108784940873081439385100251155635630",
  "points": [
    [
      "4624265727866844",
      "335925799584753674580678"
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    [
      "4631815162328502",
      "335186152589467972336848"
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    [
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    [
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  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Kazalicki - Peral (2021). Source: https://dujella.github.io/tors/z8old5.html (curve entry 57). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:24:21",
  "updated_at": "2026-09-26 20:24:21"
}