{
  "id": 5417,
  "curve_key": "0:62699939819412768",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-72569374790987"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 77.35427376546224,
  "faltings_height": 4.503845389580149,
  "conductor": "5451618715945823931151788",
  "bad_primes": [
    "2",
    "3",
    "17",
    "19",
    "383",
    "1816141"
  ],
  "discriminant": "-2275047716063647459652539561008",
  "regulator": "59222328869.399750729123761032823035043987206106457023710",
  "points": [
    [
      "50468215767/1194649",
      "2194263601190950/1305751357"
    ],
    [
      "71496940611/1050625",
      "16772618448366484/1076890625"
    ],
    [
      "861321879/7225",
      "24731032956242/614125"
    ],
    [
      "230138001/400",
      "3490597292999/8000"
    ],
    [
      "231860883",
      "-3530540747120"
    ],
    [
      "83704671993/4096",
      "-24217234464281485/262144"
    ],
    [
      "69609200289/348100",
      "-18281855533176337/205379000"
    ],
    [
      "189758423217/4545424",
      "-4207399337662825/9690843968"
    ],
    [
      "411625388361/9424900",
      "94808818435028891/28934443000"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 3-isogeny partner of curve #5413:\r\nhttps://elliptic-rank.icarm.cloud/curve/5413\r\n\r\nThe source curve was submitted by Jesper Petersen and found through Mestre’s polynomial cube-completion construction from the integer sextuple (-49,-31,-5,7,29,49). The 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.",
  "created_at": "2026-10-21 22:30:15",
  "updated_at": "2026-10-21 22:30:15"
}