{
  "id": 6002,
  "curve_key": "5542821088:339887451423104",
  "ainvs": [
    "0",
    "1",
    "0",
    "-115475439",
    "-393426745775"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 67.30730828927071,
  "faltings_height": 3.6112940348357303,
  "conductor": "362387068339061632",
  "bad_primes": [
    "2",
    "41",
    "73",
    "97",
    "223",
    "353",
    "1697"
  ],
  "discriminant": "31694367923515373587857152",
  "regulator": "235329.953935739568658153809744197287189913003087764140",
  "points": [
    [
      "-6528",
      "286793"
    ],
    [
      "-4831",
      "227398"
    ],
    [
      "12799",
      "474792"
    ],
    [
      "46079",
      "9598232"
    ],
    [
      "76625",
      "20991890"
    ],
    [
      "50253/4",
      "2981629/8"
    ],
    [
      "90981/4",
      "23661271/8"
    ],
    [
      "173737/9",
      "57728546/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rationally 2-isogenous to the rank-8 curve [0,1,0,-552775369,4641732108231] in Michael Rubinstein’s elliptic-curves-by-rank repository, torsion_Z2.add_2026-10-24.part3.tsv.gz, source index 484189.\r\n\r\nThe eight source points were transported through the degree-2 isogeny to the minimal model [0,1,0,-115475439,-393426745775]. PARI/GP returned matching rank bounds [8,8]. All eight points 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.part3.tsv.gz",
  "created_at": "2026-10-27 18:15:42",
  "updated_at": "2026-10-27 18:15:42"
}