{
  "id": 5881,
  "curve_key": "0:46569503085946887903102792",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-53899887830957046184147"
  ],
  "rank_lower_bound": 7,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 118.20597623706698,
  "faltings_height": 7.908153928880544,
  "conductor": "71866517107942728245529",
  "bad_primes": [
    "3",
    "7",
    "13",
    "19",
    "31",
    "61",
    "151",
    "181"
  ],
  "discriminant": "-1255045496337972636270420082716012177321563031363",
  "regulator": "1413777377.998769491966406195682263139908887056169902",
  "points": [
    [
      "2444929657/36",
      "-110001165712183/216"
    ],
    [
      "48092778028929/902500",
      "-267606336999866605717/857375000"
    ],
    [
      "66080285209/900",
      "15787761894931177/27000"
    ],
    [
      "1459776806881/14400",
      "1717487915577264721/1728000"
    ],
    [
      "47895225457/36",
      "10481739514266277/216"
    ],
    [
      "753901148351289/16810000",
      "13132494206912434325837/68921000000"
    ],
    [
      "136139028841/3600",
      "-2902611688771861/216000"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with b=-1 and c=-a-d. Parameters (a,d)=(-4/5,15/4) and t=d=15/4 give w=(d+1)(a^2+ad+d^2)(d^2-d+1)=16097959/25600 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, L_{a,d}(t)=(d^3+1)t^2+(3a^2d^2+ad^3-2a-3d)t-2a^2d^3+a^2+3ad+3d^2. Cubic normalization of k=(a^3+1)(t-a)w/8 gives u^3+v^3=89359770409. PARI/GP 2.17.4 ellrank bounds [7,7].",
  "created_at": "2026-10-25 19:27:54",
  "updated_at": "2026-10-25 19:27:54"
}