{
  "id": 5731,
  "curve_key": "0:322060931526024",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-372755707785"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 66.81152374382644,
  "faltings_height": 3.6252828877771655,
  "conductor": "60025025240399490517007667",
  "bad_primes": [
    "3",
    "1491022831139"
  ],
  "discriminant": "-60025025240399490517007667",
  "regulator": "605896902094.92574158969530798146174687156184039627669169",
  "points": [
    [
      "36281766113065/2258720676",
      "208481651899165166615/107347958847576"
    ],
    [
      "496992571041/126736",
      "350368330829833297/45118016"
    ],
    [
      "497009490297/31684",
      "-350386223602931929/5639752"
    ],
    [
      "497274003297/861184",
      "-350665639903437679/799178752"
    ],
    [
      "503168779041/6990736",
      "-356741273440773487/18483505984"
    ],
    [
      "527707763745/20394256",
      "-379198907521670511/92100460096"
    ],
    [
      "42425819872665/4019306404",
      "-228387718774731412295/254815987400792"
    ],
    [
      "2248780379865/302272996",
      "1037883110558647815/5255318308456"
    ],
    [
      "4662627218985/538518436",
      "6569022345479416215/12496858825816"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Constructed by specializing the Burkhardt rank-four Mordell family with parameters (u,v,w) = (7,-2,3) and t = 115/152.\r\n\r\nPARI/GP 2.17.4 computation returned matching rank bounds [9,9], together with nine rational points on the original curve.",
  "created_at": "2026-10-24 17:18:36",
  "updated_at": "2026-10-24 17:18:36"
}