{
  "id": 5528,
  "curve_key": "0:20132712",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-23302"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 33.635713025667144,
  "faltings_height": 0.8606319945972242,
  "conductor": "234563710923",
  "bad_primes": [
    "3",
    "31069"
  ],
  "discriminant": "-234563710923",
  "regulator": "1554.76509084378190608736494373365822932993925855",
  "points": [
    [
      "34",
      "126"
    ],
    [
      "52",
      "342"
    ],
    [
      "601/4",
      "14679/8"
    ],
    [
      "478",
      "10449"
    ],
    [
      "442/9",
      "8315/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Mordell curve y^2 + y = x^3 - 23302, obtained in my own bounded search of the models y^2 + t*y = x^3 + B with t = 0 or 1 and 0 < |B| <= 100000. Integer seed points were generated from B = y^2 + t*y - x^3 for integral x and y; the specialization (t,B) = (1,-23302) produced six integral seed points in the bounded search. Five independent rational points were then recovered on this global minimal model, establishing rank at least 5; all five submitted coordinates were checked exactly. The rational torsion subgroup is trivial, the conductor is 234563710923, and the minimal discriminant is -234563710923.",
  "created_at": "2026-10-22 21:59:55",
  "updated_at": "2026-10-22 21:59:55"
}