{
  "id": 5416,
  "curve_key": "0:233566042382490312",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-270331067572327"
  ],
  "rank_lower_bound": 10,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 79.98448253756942,
  "faltings_height": 4.723029453922414,
  "conductor": "260909742090503810360561327163",
  "bad_primes": [
    "3",
    "11",
    "2978854739089"
  ],
  "discriminant": "-31570078792950961053627920586723",
  "regulator": "348062853335878.4294382824592604075111038628032057905010267",
  "points": [
    [
      "3068651623057/8433216",
      "-5360429119701074887/24490059264"
    ],
    [
      "821885381304769/12421102500",
      "-6092973201392830250603/1384331873625000"
    ],
    [
      "374618115486709273/4430738724624",
      "170468605013944125923862371/9326403725100245568"
    ],
    [
      "399681500548063057/3846878131716",
      "220131451708737877327088987/7545059036128649736"
    ],
    [
      "6193390334728415569873/94001547488371524",
      "114117630541258123745394810544709/28820565946855852423058232"
    ],
    [
      "137903907521847553/1850845969764",
      "30143020365071084172194389/2517998206333191912"
    ],
    [
      "61341701101771735753/179292314240064",
      "478809739500105004047431309179/2400725522012970880512"
    ],
    [
      "1476143835388739137/122839034256",
      "1793465314812295316681545153/43053116082179904"
    ],
    [
      "175898326955359633/268894404",
      "73772170799038240826342179/4409330436792"
    ],
    [
      "318629506058416177/4472692035876",
      "-90336145846242774053658437/9459180096681219624"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 3-isogeny partner of curve #5414:\r\nhttps://elliptic-rank.icarm.cloud/curve/5414\r\n\r\nThe source curve was submitted by Jesper Petersen and obtained through Mestre’s polynomial cube-completion construction from the integer sextuple (-45,-13,-1,9,11,39). The ten source points were transported through the exact degree-3 isogeny and checked exactly on this minimal target model. Rank ≥10 is preserved under the rational isogeny. Rational torsion is trivial.",
  "created_at": "2026-10-21 22:27:37",
  "updated_at": "2026-10-21 22:27:37"
}