{
  "id": 5420,
  "curve_key": "0:639644985546797339452408001566948220448",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-740329844382867291032879631443227107"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 178.70795332029536,
  "faltings_height": 12.949985352482908,
  "conductor": "239866869580049002294653000587605582668",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "19",
    "29",
    "37",
    "43",
    "67",
    "193",
    "271",
    "1777"
  ],
  "discriminant": "-236774136305070935927742001842924216395473692722976504185303410627982641968",
  "regulator": "6397320781247045.7390411558872462759618403308187980537730",
  "points": [
    [
      "2028713932851056140057/2067339024",
      "42524035227073375201246308462845/93997770743232"
    ],
    [
      "23007932238171835814034211/6028817283225",
      "109623749113536657383891697293184111584/14802946948625752125"
    ],
    [
      "457776405282836281149814513/499250045961216",
      "1950853536257237467938064269429399774665/11155195098952998027264"
    ],
    [
      "786986085147418769590900961577499/19932684367566215025",
      "22077402137372719870830238748617470007976376596068/88991532292167988244536512375"
    ],
    [
      "1769612121827451443226854025367681/1955441554527735014400",
      "-2459878751906640211386962308459024011258613796671/86470358597146403694070198272000"
    ],
    [
      "230079986525634737445337280945376199/253170536364267142763025",
      "-12896950967793880743527018860833116671802055014767418/127385425638545060397872228917397625"
    ],
    [
      "2969775370500543564639868895549999618617/1674022563905978874439898244",
      "150728544044389301460813134721243126772431353912880736739315/68492333274852260495697639614011901102472"
    ],
    [
      "2726782314633504708568691395801420655103607/2042301960018776311934088758049",
      "3737392959916626447135953731970263092604291919291390449325185510/2918635974670789626371781198078318066926459343"
    ],
    [
      "129172699560849244126996872181193941389618483946999/8111011001191670833070286458860697025",
      "1467967022561198042756040670978598002792983569764278547639895694374132188318/23100026902229616281756210283168489737169416428011902625"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 3-isogeny partner of curve #3081:\r\nhttps://elliptic-rank.icarm.cloud/curve/3081\r\n\r\nThe source curve is attributed to Voznyy (2023) in Dujella’s Z/3Z table, curve entry 58:\r\nhttps://dujella.github.io/tors/z3old891011121314.html\r\n\r\nThe nine source points were transported through the exact degree-3 isogeny and checked exactly on this minimal target model. Rank ≥9 is preserved under the rational isogeny. Rational torsion is trivial. This target is a cube-sum curve.",
  "created_at": "2026-10-21 22:42:51",
  "updated_at": "2026-10-21 22:42:51"
}