{
  "id": 5436,
  "curve_key": "-3120:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "65",
    "0"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 24.136764842410585,
  "faltings_height": 0.07963748184237242,
  "conductor": "270400",
  "bad_primes": [
    "2",
    "5",
    "13"
  ],
  "discriminant": "-17576000",
  "regulator": "10.6312842340253314507900915727765398023094",
  "points": [
    [
      "4",
      "18"
    ],
    [
      "1040",
      "33540"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Quartic twist y^2=x^3+65x. PARI/GP 2.17.4 returned rank bounds [2,2] with generators [4,18] and [1040,33540], rational torsion Z/2Z generated by [0,0], conductor 270400, minimal discriminant -17576000, and bad primes 2, 5 and 13. Found in a bounded exact small-coefficient quartic-twist sweep.",
  "created_at": "2026-10-22 00:02:46",
  "updated_at": "2026-10-22 00:02:46"
}