{
  "id": 5991,
  "curve_key": "-18791733895856:-41754870778635911168",
  "ainvs": [
    "0",
    "-1",
    "0",
    "391494456164",
    "48327266236380250"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 91.69331460805023,
  "faltings_height": 5.727634773989245,
  "conductor": "11171497840104689215302720",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "47",
    "59",
    "131",
    "811",
    "426841",
    "1016929"
  ],
  "discriminant": "-4849178455645804448466858007738006080",
  "regulator": "1331027209.813534174209956747327895347269894194190008977525",
  "points": [
    [
      "172475",
      "347823180"
    ],
    [
      "27198699",
      "141885363128"
    ],
    [
      "-19506931/196",
      "251160500697/2744"
    ],
    [
      "-9580791/256",
      "751068143077/4096"
    ],
    [
      "-2819669/81",
      "135713242268/729"
    ],
    [
      "-475971/4",
      "60609761/8"
    ],
    [
      "514699/225",
      "748784970568/3375"
    ],
    [
      "4966389/4",
      "12517905139/8"
    ],
    [
      "24339699/25",
      "145361556232/125"
    ],
    [
      "34097621/4",
      "199650182499/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "The rationally 2-isogenous partner of [0,-1,0,-1778840500281,410286614865460281] from Michael Rubinstein’s elliptic-curves-by-rank repository, torsion_Z2.add_2026-10-24.part3.tsv.gz, data row 546627.\r\n\r\nReduction gives the global minimal model [0,-1,0,391494456164,48327266236380250]. 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 17:14:24",
  "updated_at": "2026-10-27 17:14:24"
}