{
  "id": 4858,
  "curve_key": "0:-17496",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "20"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    3
  ],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 19.539455124713207,
  "faltings_height": -0.31405616381560403,
  "conductor": "243",
  "bad_primes": [
    "3"
  ],
  "discriminant": "-177147",
  "regulator": "1.519102066140296879158950360729232392223",
  "points": [
    [
      "-2",
      "3"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Elkies and Rogers (2004), Elliptic Curves x^3+y^3=k of High Rank: https://arxiv.org/abs/math/0403116. This is the rational 3-isogenous partner of the cube-sum curve with k=9. I recovered one rational point with PARI/GP and checked it exactly on this minimal model. PARI/GP returned matching rank bounds [1,1]. Rational torsion Z/3Z. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:11:26",
  "updated_at": "2026-10-20 22:11:26"
}