{
  "id": 5595,
  "curve_key": "0:-650445026915448",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "752829892263"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 68.21735580268138,
  "faltings_height": 3.74243555934841,
  "conductor": "244837229767961732153553843",
  "bad_primes": [
    "3",
    "283",
    "10640705191"
  ],
  "discriminant": "-244837229767961732153553843",
  "regulator": "12614262728081.69263292029988627474180475272364969645887713",
  "points": [
    [
      "-46313722529223/5699344036",
      "200073707530023865833/430266278653784"
    ],
    [
      "-658909402503/102292996",
      "720929688190981703/1034591361544"
    ],
    [
      "-35029616073623/11600582436",
      "1064086894648844039177/1249452331851816"
    ],
    [
      "-391917915423/149915536",
      "1573629509951020593/1835565822784"
    ],
    [
      "-216372525207/177369124",
      "2047108869590738679/2362201993432"
    ],
    [
      "1291611574377/13524294436",
      "1364647092674864538673/1572794297140184"
    ],
    [
      "51523685077593/19763298724",
      "2438872196548851425881/2778364061217368"
    ],
    [
      "1719286391649/405619600",
      "7437911110301520143/8169178744000"
    ],
    [
      "2232875906217/455139556",
      "9061542768557156913/9709947287704"
    ],
    [
      "2374155791649/468289600",
      "9523284499483654607/10133786944000"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "The rational 3-isogenous partner of our accepted rank-10 Mordell curve obtained from the Burkhardt quartic with parameters (u,v,w) = (7,-2,3), specialized at t = -208/211.\r\n\r\nConstructed using the rational 3-isogeny y² = x³+B → y² = x³−27B. Rank is exactly 10 because the original curve has certified exact rank 10 and isogenous elliptic curves have equal Mordell–Weil rank.",
  "created_at": "2026-10-23 21:40:30",
  "updated_at": "2026-10-23 21:40:30"
}