{
  "id": 2691,
  "curve_key": "70130676712127596370497:-24012937362124644096864282951339361",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1461055764835991591052",
    "27792751576411398242819550412944"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    9
  ],
  "naive_height": 158.32780162133548,
  "faltings_height": 11.206053096899387,
  "conductor": "1192831413867834",
  "bad_primes": [
    "2",
    "3",
    "13",
    "19",
    "23",
    "31",
    "47",
    "127",
    "379",
    "499"
  ],
  "discriminant": "-134083694914877524631235431053014505424287198533133512496568572416",
  "regulator": "4133.1175508327053162002128063084464621367941",
  "points": [
    [
      "905006188194/25",
      "590827032248766912/125"
    ],
    [
      "4283836168008/121",
      "6017734641259276332/1331"
    ],
    [
      "262114670331012918/83521",
      "134185271883391621596857178/24137569"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Voznyy (2021). Source: https://dujella.github.io/tors/z9old3.html (curve entry 16). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:17:56",
  "updated_at": "2026-09-26 20:17:56"
}