{
  "id": 5722,
  "curve_key": "0:-6345310916536463647800",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "7344109857102388481"
  ],
  "rank_lower_bound": 12,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 100.40400610931792,
  "faltings_height": 6.424656418234789,
  "conductor": "1278481768134837687888432658099974675",
  "bad_primes": [
    "3",
    "5",
    "19181",
    "756315294737"
  ],
  "discriminant": "-23300330224257416861766685193872038451875",
  "regulator": "148542158347.77049875037519649278631823836639296944983655693820",
  "points": [
    [
      "-2091879/4",
      "21467861015/8"
    ],
    [
      "-451799/4",
      "21677887545/8"
    ],
    [
      "252009",
      "2712953110"
    ],
    [
      "701569",
      "2772980609"
    ],
    [
      "1196811",
      "3009712603"
    ],
    [
      "11091609/4",
      "42831703319/8"
    ],
    [
      "4285899",
      "9277472155"
    ],
    [
      "8153541",
      "23439142426"
    ],
    [
      "18839259",
      "81815219860"
    ],
    [
      "-24134949/25",
      "317321935799/125"
    ],
    [
      "-17463221/9",
      "5310444916/27"
    ],
    [
      "59862609/169",
      "5971861947037/2197"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Constructed from the rational Bruin–Nasserden parametrization of the Burkhardt quartic with parameters (u,v,w)=(3/5,16/5,-14/5) and specialization t=1102/751. The specialization was selected using a three-stage Mestre–Nagao sieve involving 328 primes, followed by rational-point reconstruction. All twelve points were verified by exact arithmetic on the minimal model. PARI/GP 2.17.4 returned matching computational rank bounds [12,12].",
  "created_at": "2026-10-24 16:53:37",
  "updated_at": "2026-10-24 16:53:37"
}