{
  "id": 6006,
  "curve_key": "16729136212288:-68394300156244218880",
  "ainvs": [
    "0",
    "1",
    "0",
    "-348523671089",
    "79159953450725631"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 91.34451899558903,
  "faltings_height": 5.356201254226496,
  "conductor": "201673312466208",
  "bad_primes": [
    "2",
    "3",
    "11",
    "17",
    "83",
    "229",
    "239",
    "2473"
  ],
  "discriminant": "2374222478046588848823402578817024",
  "regulator": "14324.328827194646035939397725305159997484422893453",
  "points": [
    [
      "-597285",
      "272483436"
    ],
    [
      "241771",
      "95023092"
    ],
    [
      "291235",
      "48576396"
    ],
    [
      "346882",
      "1672845"
    ],
    [
      "1439053/4",
      "147097005/8"
    ],
    [
      "3014995/9",
      "3565988/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rationally 2-isogenous to the rank-6 curve [0,1,0,-25527082394,782570227763016] in Michael Rubinstein’s elliptic-curves-by-rank repository, torsion_Z2xZ2.add_2026-10-24.tsv.gz, source index 114 (115th data row).\r\n\r\nThe source points were transported through the degree-2 isogeny to the minimal model [0,1,0,-348523671089,79159953450725631]. Using these points, PARI/GP returned matching rank bounds [6,6] and the six independent points listed here. All six were checked exactly on this model. Rational torsion Z/4Z.\r\n\r\nSource: https://github.com/mrubinst/elliptic-curves-by-rank/blob/5e2e867ddb468765263bfadf520d9acda17a5a4b/torsion/torsion_Z2xZ2.add_2026-10-24.tsv.gz",
  "created_at": "2026-10-27 18:45:47",
  "updated_at": "2026-10-27 18:45:47"
}