{
  "id": 6244,
  "curve_key": "0:70366092804870189814520762097527305801063200",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-81442237042673830803843474649915863195675"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 201.92457083319087,
  "faltings_height": 14.884703478557535,
  "conductor": "325768948170695323215373898599663452782700",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "23",
    "41",
    "71",
    "139",
    "173",
    "179",
    "241",
    "443"
  ],
  "discriminant": "-2865386004990511745895882069092661965384978964982953271515747410376675754082320830000",
  "regulator": "12714612799275.922221711804877492500527111798841628569510",
  "points": [
    [
      "51839991328351",
      "240565505734184408126"
    ],
    [
      "103858170857599",
      "1019228121732074011318"
    ],
    [
      "152362235374771",
      "1858906372731237541844"
    ],
    [
      "253552470959299",
      "4027301321930632444168"
    ],
    [
      "15069209907797179/169",
      "-1740352391629869202567208/2197"
    ],
    [
      "1752258941206771489/22500",
      "-2110089534197705208243709487/3375000"
    ],
    [
      "7849245647531189689/128164",
      "17667571744251216592173902413/45882712"
    ],
    [
      "42176318646208498201/722500",
      "-210497269878982998511955806051/614125000"
    ],
    [
      "94273687919030291690881/1441872784",
      "24366468605270559900205808810029121/54750793354048"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 3-isogeny partner of the Choudhry–Shamsi Zargar–Voznyy (2023) rank-9 curve y^2 = x^3 + 3016379149728660400142350912959846785025, listed in the rank-9 section of Dujella’s Z/3Z table:\r\nhttps://dujella.github.io/tors/z3old891011121314.html\r\n\r\nThe nine source points were transported through the exact degree-3 isogeny (x, y) ↦ ((x^3 + 4B)/x^2, y(x^3 − 8B)/x^3) and checked exactly on this minimal target model. Rank ≥9 is preserved under the rational isogeny. This target is a cube-sum curve.",
  "created_at": "2026-10-31 21:38:50",
  "updated_at": "2026-10-31 21:38:50"
}