{
  "id": 5678,
  "curve_key": "0:25506053930230646472",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-29520895752581767"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 89.37089501381759,
  "faltings_height": 5.50523049360976,
  "conductor": "2832432250889733342553290483",
  "bad_primes": [
    "3",
    "7",
    "61",
    "23986672649"
  ],
  "discriminant": "-376480779567033684957896798446207203",
  "regulator": "87575557044820.40305273532473645919580545434394231804371052",
  "points": [
    [
      "896314903801/2755600",
      "319970590931237549/4574296000"
    ],
    [
      "1170079555633/195364",
      "1265590617608197661/86350888"
    ],
    [
      "1175346310273/484",
      "1274232777657301821/10648"
    ],
    [
      "97265526278929/109411600",
      "-938894776972298531033/1144445336000"
    ],
    [
      "2339466827161/6100900",
      "-2469918815834805841/15069223000"
    ],
    [
      "422973797558929/1314787600",
      "2928642859247339983783/47674198376000"
    ],
    [
      "418539123697/948676",
      "219346276486559413/924010424"
    ],
    [
      "908575011397202857/2910149399056",
      "-149884729876955115296122613/4964470422240015296"
    ],
    [
      "25718341550693521/25430680900",
      "-4065150212278034760977819/4055430683123000"
    ],
    [
      "78992488433497/247307076",
      "215360581045228949087/3889151077176"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Exact-rank-10 Mordell curve discovered in October 2026 using the Burkhardt quartic construction, with parameters (u,v,w)=(3,2,1) and specialization t=-221/770.\r\n\r\nExact rank [10,10] independently verified with PARI/GP 2.17.4 using ten rational points checked exactly on the minimal model.",
  "created_at": "2026-10-24 07:36:45",
  "updated_at": "2026-10-24 07:36:45"
}