{
  "id": 5679,
  "curve_key": "0:19808812742035566312",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-22926866599578202"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 88.86531720110527,
  "faltings_height": 5.463099009217068,
  "conductor": "3438053538448260349218292587",
  "bad_primes": [
    "3",
    "7",
    "43",
    "383",
    "32627809"
  ],
  "discriminant": "-227077003616337159370754837945919723",
  "regulator": "46981176007.80580709179693577479071338781438088807962287107",
  "points": [
    [
      "299538",
      "62837770"
    ],
    [
      "424102",
      "230983077"
    ],
    [
      "23452353/16",
      "113160007615/64"
    ],
    [
      "57173617/196",
      "119422513813/2744"
    ],
    [
      "296894962/81",
      "5114499257773/729"
    ],
    [
      "303978438/961",
      "2782230727099/29791"
    ],
    [
      "698948488/1369",
      "16811678386121/50653"
    ],
    [
      "65625076897/91204",
      "16285908291911115/27543608"
    ],
    [
      "160623750924/87025",
      "64257144615294907/25672375"
    ],
    [
      "1251949282542/1125721",
      "1389089556313686482/1194389981"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Exact-rank-10 Mordell curve discovered in October 2026 using the Burkhardt quartic construction, with parameters (u,v,w)=(-3,2,-4) and specialization t=685/209.\r\n\r\nExact rank [10,10] independently verified with PARI/GP 2.17.4 using ten rational points checked exactly on the minimal model.",
  "created_at": "2026-10-24 07:38:15",
  "updated_at": "2026-10-24 07:38:15"
}