{
  "id": 5680,
  "curve_key": "0:-733659731186502456",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "849143207391785"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 82.27364346909661,
  "faltings_height": 4.913792864883012,
  "conductor": "3438053538448260349218292587",
  "bad_primes": [
    "3",
    "7",
    "43",
    "383",
    "32627809"
  ],
  "discriminant": "-311491088636950835899526526674787",
  "regulator": "2774191462084925.102963517260565616834837051377060213650914",
  "points": [
    [
      "-432880064615/5391684",
      "227985526228058497/12519490248"
    ],
    [
      "-314845259333951/33035970564",
      "174883804680830621193179/6004551937771512"
    ],
    [
      "154610641899919525105/977800642198416",
      "2118896034165447656192820218071/30575634432618597430464"
    ],
    [
      "-272376563089807143911/3118552112624004",
      "2355074553341602464596702814239/174152417940270654127992"
    ],
    [
      "288314144774907545641/709251386387076",
      "4926366190687532297083027466113/18888622631447284552824"
    ],
    [
      "-355896264254054946455/5336168381042724",
      "9162156789444689425217999653705/389802201632597190979368"
    ],
    [
      "1171734635152553234809/66435973907125824",
      "500603506955765901251096611258189/17123989733363548934456832"
    ],
    [
      "115224653220326025649271542825/1911873417276637128313476",
      "86394171740963975979315618458120778161688961/2643557141015236947898284402087343224"
    ],
    [
      "556455492234011787051170929/2753518877191573779600",
      "13785129313082209674370206670367325282967/144488102366437087447155817656000"
    ],
    [
      "249561145096264451387671819681/2163857905218086285791716",
      "155390475684608279363279065001662218593307923/3183047412436562426926997683212060264"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Exact-rank-10 Mordell curve obtained by rational 3-isogeny from the Burkhardt specialization with parameters (u,v,w)=(-3,2,-4) and t=685/209, 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.\r\n",
  "created_at": "2026-10-24 07:39:09",
  "updated_at": "2026-10-24 07:39:09"
}