{
  "id": 5786,
  "curve_key": "0:-12460937507380728",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "14422381374283"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 74.12275029360464,
  "faltings_height": 4.234551766925349,
  "conductor": "89858196506277679791362931603",
  "bad_primes": [
    "3",
    "317",
    "523",
    "6827",
    "50969"
  ],
  "discriminant": "-89858196506277679791362931603",
  "regulator": "41615892555174.85145421216440413324395849434959699215608230",
  "points": [
    [
      "-1651",
      "3797088"
    ],
    [
      "-521741928965054686439039/26399974808284736400",
      "351200122800986896458504184553013791/135645461874685110054623112000"
    ],
    [
      "-83425337670509/4233714489",
      "716827536616222188703/275475100655763"
    ],
    [
      "161867331011/6235009",
      "87959667927432093/15568817473"
    ],
    [
      "2263891834289/1608010000",
      "244902692985139259337/64481201000000"
    ],
    [
      "5443359831319/111070521",
      "13455473055022612619/1170572220819"
    ],
    [
      "5866341936611/16589329",
      "14210909406535128226/67568337017"
    ],
    [
      "473319697834289/12973210000",
      "11727276095875627259337/1477648619000000"
    ],
    [
      "68778968661908423/87852367201",
      "18038067805349801525150575/26039353786009199"
    ],
    [
      "55773473549276376425057/13556191115072835856",
      "190007602158089302267067429080321487/49912178333182959734654418496"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "The rationally 3-isogenous partner of a specialization of a generic rank-four Burkhardt Mordell family.\r\n\r\nThe underlying Burkhardt construction uses parameter triple (3,8,-6), with the sextic parameter specialized at t=-402/499.",
  "created_at": "2026-10-25 08:37:19",
  "updated_at": "2026-10-25 08:37:19"
}