{
  "id": 6005,
  "curve_key": "286110688:865116563840",
  "ainvs": [
    "0",
    "1",
    "0",
    "-5960639",
    "-1003279199"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 58.415667944669536,
  "faltings_height": 2.9342423796101618,
  "conductor": "1232620115650432",
  "bad_primes": [
    "2",
    "17",
    "47",
    "137",
    "281",
    "337",
    "929"
  ],
  "discriminant": "13120602633878941716224",
  "regulator": "17253.60482896741149875599684940908687095666396311952",
  "points": [
    [
      "-1679",
      "65378"
    ],
    [
      "-1424",
      "67817"
    ],
    [
      "-296",
      "27115"
    ],
    [
      "3376",
      "131767"
    ],
    [
      "-99504/49",
      "17925055/343"
    ],
    [
      "-3683/4",
      "486965/8"
    ],
    [
      "-987/4",
      "170185/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rationally 2-isogenous to the rank-7 curve [0,1,0,-59183049,174279405895] in Michael Rubinstein’s elliptic-curves-by-rank repository, torsion_Z2.add_2026-10-24.part1.tsv.gz, source index 588815.\r\n\r\nThe source points were transported through the degree-2 isogeny to the minimal model [0,1,0,-5960639,-1003279199]. Using these points, PARI/GP returned matching rank bounds [7,7] and the seven independent points listed here. All seven were checked exactly on this model. Rational torsion Z/2Z.\r\n\r\nSource: https://github.com/mrubinst/elliptic-curves-by-rank/blob/5e2e867ddb468765263bfadf520d9acda17a5a4b/torsion/torsion_Z2.add_2026-10-24.part1.tsv.gz",
  "created_at": "2026-10-27 18:38:21",
  "updated_at": "2026-10-27 18:38:21"
}