{
  "id": 5419,
  "curve_key": "0:2036530133150667942766335222780904392",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-2357095061516976785609184285626047"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell",
    "cubesum"
  ],
  "naive_height": 167.20862158464203,
  "faltings_height": 11.991707707845132,
  "conductor": "9428380246067907142436737142504187",
  "bad_primes": [
    "3",
    "13",
    "23",
    "31",
    "43",
    "61",
    "73",
    "157",
    "199",
    "337"
  ],
  "discriminant": "-2400147559739975289389017909330207968162256197313345424663195438336163",
  "regulator": "14491371161687.368190809110772593034016550629214360173765",
  "points": [
    [
      "9165790760857/36",
      "25691656666726201967/216"
    ],
    [
      "2266728229583089/14400",
      "-67884684612841020677687/1728000"
    ],
    [
      "5930433056062369/44100",
      "80091480203512336805653/9261000"
    ],
    [
      "465422286186947521/57600",
      "-317519054363650281653812319/13824000"
    ],
    [
      "305179215546861457/1806336",
      "-120542171581739587677113017/2427715584"
    ],
    [
      "578681535808377193/627264",
      "439548278760254029519448011/496793088"
    ],
    [
      "1543199831042552329/2722500",
      "-1904603169274062219408348017/4492125000"
    ],
    [
      "91424327845739082697/557715456",
      "596039985484721722141704137467/13171008208896"
    ],
    [
      "798766994672348195257/5601624336",
      "9763829185288386618997938253043/419247971803584"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 3-isogeny partner of curve #3080:\r\nhttps://elliptic-rank.icarm.cloud/curve/3080\r\n\r\nThe source curve is attributed to Elkies–Rogers (2004) in Dujella’s Z/3Z table, curve entry 51:\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 22:36:25",
  "updated_at": "2026-10-21 22:36:25"
}