{
  "id": 6245,
  "curve_key": "0:3429927739260989445714821265477718347018688800",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-3969823772292811858466228316525136975716075"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 209.69773675683427,
  "faltings_height": 15.532467305527819,
  "conductor": "15879295089171247433864913266100547902864300",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "23",
    "29",
    "47",
    "317",
    "1223",
    "1667",
    "6037"
  ],
  "discriminant": "-6808104338282408564788840147310618128443681433533485579031749440042206235119893791230000",
  "regulator": "83171722247496.068551851631032122549121725177760285488756",
  "points": [
    [
      "734586362675401/4",
      "11930073725579527087451/8"
    ],
    [
      "3970250802341179/25",
      "23540091736407140365408/125"
    ],
    [
      "1881429910393668199/11881",
      "-45313045240281217674738218/1295029"
    ],
    [
      "4670072855194578019/9409",
      "-9927012525553764254254730572/912673"
    ],
    [
      "27024051690593996569/4624",
      "140482224612045532748254611203/314432"
    ],
    [
      "536153151393105618601/665856",
      "-12367325285192250086520281836949/543338496"
    ],
    [
      "788663354413455810931/3352561",
      "-18464860336064394107634952732804/6138539191"
    ],
    [
      "153014537119008626767291/459544969",
      "56544997946969083193423758869997636/9851265500453"
    ],
    [
      "7120901493488988849244991899/2109666195961",
      "600869347545702191088399317980564091416568/3064224749981277709"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 3-isogeny partner of the Choudhry–Shamsi Zargar–Voznyy (2023) rank-9 curve y^2 = x^3 + 147030510084918957720971419130560628730225, 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 21:39:58",
  "updated_at": "2026-10-31 21:39:58"
}