{
  "id": 5431,
  "curve_key": "5616:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-117",
    "0"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 25.90012483711694,
  "faltings_height": 0.22658414806790217,
  "conductor": "48672",
  "bad_primes": [
    "2",
    "3",
    "13"
  ],
  "discriminant": "102503232",
  "regulator": "1.21444623643124316026436700738605498694004",
  "points": [
    [
      "-9",
      "18"
    ],
    [
      "-3",
      "18"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 - 117x. PARI/GP 2.17.4 returned rank bounds [2,2] with generators [-9,18] and [-3,18], rational torsion Z/2Z generated by [0,0], conductor 48672, minimal discriminant 102503232, and bad primes 2, 3 and 13. Found in a bounded exact small-coefficient quartic-twist sweep.",
  "created_at": "2026-10-21 23:52:37",
  "updated_at": "2026-10-21 23:52:37"
}