{
  "id": 5484,
  "curve_key": "-43392:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "904",
    "0"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 32.0340911139002,
  "faltings_height": 0.7377480044665072,
  "conductor": "3268864",
  "bad_primes": [
    "2",
    "113"
  ],
  "discriminant": "-47280848896",
  "regulator": "47.226323594849806386879126053903967925462420",
  "points": [
    [
      "8",
      "88"
    ],
    [
      "225",
      "3405"
    ],
    [
      "392",
      "7784"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of ICARM curve #5479:\r\nhttps://elliptic-rank.icarm.cloud/curve/5479\r\n\r\nApplying the standard 2-isogeny y^2 = x^3 + Ax → y^2 = x^3 − 4Ax to A = −226 gives y^2 = x^3 + 904x. This endpoint was also recovered independently in an exact bounded quartic sweep over 301 <= |A| <= 1500.\r\n\r\nPARI/GP 2.17.4 returned rank bounds [3,3], rational torsion Z/2Z generated by [0,0], conductor 3268864 and minimal discriminant -47280848896. Exact quadratic-character certification at 10 good primes gives an F_2 matrix of rank 4 with torsion-row rank 1, proving the three submitted points independent modulo torsion.",
  "created_at": "2026-10-22 10:08:52",
  "updated_at": "2026-10-22 10:08:52"
}