{
  "id": 5830,
  "curve_key": "0:6207994195563232800",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-7185178467087075"
  ],
  "rank_lower_bound": 5,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 86.54473904356054,
  "faltings_height": 5.26971749608834,
  "conductor": "28740713868348300",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "37"
  ],
  "discriminant": "-22302773108881244173023393048030000",
  "regulator": "21238.3635736601577062395256799839219396225474822",
  "points": [
    [
      "2750839",
      "4561658738"
    ],
    [
      "831649/4",
      "339632657/8"
    ],
    [
      "4286191/9",
      "8573533514/27"
    ],
    [
      "6589219/9",
      "16758622972/27"
    ],
    [
      "10043761/16",
      "31364874359/64"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Burkhardt quartic 1+a^3+b^3+c^3+d^3+3abcd=0, with (a,b,c,d)=(17,-10,-7,-1) and specialization t=23/7. The square-condition construction yields, via 3-isogeny and rational cubic scaling, the cubesum curve u^3+v^3=32626230. PARI/GP 2.17.4 returned matching computational rank bounds [5,5].",
  "created_at": "2026-10-25 11:03:05",
  "updated_at": "2026-10-25 11:03:05"
}