{
  "id": 5478,
  "curve_key": "-22464:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "468",
    "0"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 30.059007920476613,
  "faltings_height": 0.5731577383478749,
  "conductor": "48672",
  "bad_primes": [
    "2",
    "3",
    "13"
  ],
  "discriminant": "-6560206848",
  "regulator": "4.85778494572497264105746802954421994776016",
  "points": [
    [
      "4",
      "-44"
    ],
    [
      "36",
      "-252"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of ICARM curve #5431:\r\nhttps://elliptic-rank.icarm.cloud/curve/5431\r\n\r\nThe source curve was submitted by The Wren after a bounded exact small-coefficient quartic-twist sweep. Applying the standard 2-isogeny y^2 = x^3 + Ax → y^2 = x^3 − 4Ax with A = −117 gives y^2 = x^3 + 468x. The two source points map exactly to (4,−44) and (36,−252).\r\n\r\nPARI/GP 2.17.4 returned rank bounds [2,2], rational torsion Z/2Z, conductor 48672 and minimal discriminant -6560206848. Exact quadratic-character certification at 8 good primes gives an F_2 matrix of rank 3 with torsion-row rank 1, proving the two submitted points independent modulo torsion.",
  "created_at": "2026-10-22 09:30:25",
  "updated_at": "2026-10-22 09:30:25"
}