{
  "id": 5992,
  "curve_key": "-23079750973472:-48571742777142865024",
  "ainvs": [
    "0",
    "1",
    "0",
    "480828145281",
    "56217455157000817"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 92.30993030339796,
  "faltings_height": 5.774484275531328,
  "conductor": "16316460421276568501222528",
  "bad_primes": [
    "2",
    "23",
    "73",
    "89",
    "127",
    "449",
    "457",
    "2393",
    "3313",
    "4129"
  ],
  "discriminant": "-8479871732389273259160578371133540608",
  "regulator": "91840384.24927822248771999060574585669674836507138430650454",
  "points": [
    [
      "5801",
      "242913430"
    ],
    [
      "369849",
      "533518894"
    ],
    [
      "465257",
      "616958474"
    ],
    [
      "1820943",
      "2640023684"
    ],
    [
      "8216184",
      "23635692109"
    ],
    [
      "15742169",
      "62520278974"
    ],
    [
      "-50979/4",
      "1790416277/8"
    ],
    [
      "5081784/25",
      "50366641177/125"
    ],
    [
      "14831377/9",
      "62298294722/27"
    ],
    [
      "68505856/25",
      "585634096821/125"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "The rationally 2-isogenous partner of [0,1,0,-2117735364649,470396776165021671] from Michael Rubinstein’s elliptic-curves-by-rank repository, torsion_Z2.add_2026-10-24.part3.tsv.gz, data row 546637.\r\n\r\nReduction gives the global minimal model [0,1,0,480828145281,56217455157000817]. PARI/GP returned matching rank bounds [10,10] and the ten rational points listed here. All ten were checked exactly on this model. Rational torsion Z/2Z.\r\n\r\nSource:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank/blob/5e2e867ddb468765263bfadf520d9acda17a5a4b/torsion/torsion_Z2.add_2026-10-24.part3.tsv.gz",
  "created_at": "2026-10-27 17:18:24",
  "updated_at": "2026-10-27 17:18:24"
}