{
  "id": 5870,
  "curve_key": "0:13317595523348882119200",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-15413883707579724675"
  ],
  "rank_lower_bound": 6,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 101.88674617085417,
  "faltings_height": 6.548218090029476,
  "conductor": "20551844943439632900",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "29",
    "31",
    "37",
    "59"
  ],
  "discriminant": "-102637934330742005455177698736283265630000",
  "regulator": "5114267.1200902346719350319173761717390410414527332",
  "points": [
    [
      "151523409/16",
      "1848172806873/64"
    ],
    [
      "4073259",
      "-7222696452"
    ],
    [
      "2519031",
      "-755427546"
    ],
    [
      "14255481/4",
      "43709178771/8"
    ],
    [
      "33118339/9",
      "-158392803988/27"
    ],
    [
      "3593967969/1444",
      "3412345768497/54872"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, on b=-1, c=-a-d. Specialization (a,b,c,d)=(-2,-1,-1,3), t=1249/393, w=36386126/154449 on w^2=D_{a,d}(t), where D_{a,d}(t)=L_{a,d}(t)^2-4(a^3+1)d^3(t-a)(t-d)^3 and the cubesum parameter k=(a^3+1)(t-a)w/8 up to rational cubic scaling, yields u^3+v^3=1511138090. PARI/GP 2.17.4 ellrank bounds [6,6].",
  "created_at": "2026-10-25 17:51:20",
  "updated_at": "2026-10-25 17:51:20"
}