{
  "id": 5681,
  "curve_key": "0:30544637177935944",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-35352589326315"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 75.91593104532365,
  "faltings_height": 4.383983496235265,
  "conductor": "3672898007730799119448602321",
  "bad_primes": [
    "3",
    "7",
    "2885925659291"
  ],
  "discriminant": "-539916007136427470558944541187",
  "regulator": "3061070604506797.867549394859415010958739598658131694521061",
  "points": [
    [
      "81604371605425/586705284",
      "-732315585050433368045/14211175389048"
    ],
    [
      "1156805376704017721/2292147552256",
      "1244029613358160264489112173/3470274719754747904"
    ],
    [
      "42630151541724941808879714305537/1011996953437890546464755264",
      "202071160991430598480030723825206870681723926017/32193545434966675268411717132619687142912"
    ],
    [
      "425843414053455263604598591062913/11414195956047153455012610576",
      "4964999948196318902833835673277769418664753508063/1219461198384456752640289424045440646026176"
    ],
    [
      "1637560360401728393/11305236130276",
      "2083316379485714391038567143/38011889376966381976"
    ],
    [
      "3635371526165233873/141161009796",
      "6931435742825733257144720347/53036167634494344"
    ],
    [
      "493521445795844825/14929599565456",
      "-50605107787083538329674819/57686240887372391104"
    ],
    [
      "94850435732322264121/2416311352880100",
      "-595470765143625671613528131831/118776176699060666799000"
    ],
    [
      "6551196505686885235685273/197914536149288935876",
      "2664570176766304961145744130217313673/2784303281538019655390507880376"
    ],
    [
      "161307579178941882189556545097/3750034854097208084106384",
      "48300061762784728478153932306084530299458459/7261945016377678373920006542777622848"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Exact-rank-10 Mordell curve obtained by rational 3-isogeny from the Burkhardt specialization with parameters (u,v,w)=(2,-1,1) and t=958/647, discovered in October 2026.\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 07:40:44",
  "updated_at": "2026-10-24 07:40:44"
}