{
  "id": 5993,
  "curve_key": "-224329240679:-143911595004812605",
  "ainvs": [
    "1",
    "0",
    "1",
    "4673525847",
    "166564735530872"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 79.0159511647615,
  "faltings_height": 4.6847821605802995,
  "conductor": "53548916157398492398",
  "bad_primes": [
    "2",
    "17",
    "47",
    "59",
    "103",
    "149",
    "191",
    "239",
    "463"
  ],
  "discriminant": "-18518289350613785040271651676188",
  "regulator": "335822.91740667883093747186088352237597124094879381879797",
  "points": [
    [
      "-21122",
      "7654335"
    ],
    [
      "-1711",
      "12593048"
    ],
    [
      "34338",
      "19153966"
    ],
    [
      "43221",
      "21175060"
    ],
    [
      "485735/4",
      "401491229/8"
    ],
    [
      "268981",
      "144380758"
    ],
    [
      "-2408699/121",
      "10797005810/1331"
    ],
    [
      "1353224/25",
      "3002167472/125"
    ],
    [
      "28060105/256",
      "182757975571/4096"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "The rationally 2-isogenous partner of [1,0,1,-32115842143,1707229888216092] from Michael Rubinstein’s elliptic-curves-by-rank repository, torsion_Z2.add_2026-10-24.part3.tsv.gz, data row 544594.\r\n\r\nReduction gives the global minimal model [1,0,1,4673525847,166564735530872]. PARI/GP returned matching rank bounds [9,9] and the nine rational points listed here. All nine 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 17:24:40",
  "updated_at": "2026-10-27 17:24:40"
}