{
  "id": 5350,
  "curve_key": "49417282674816:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1029526722392",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 94.59396399196652,
  "faltings_height": 5.951070744305367,
  "conductor": "4239701088476856936806656",
  "bad_primes": [
    "2",
    "7",
    "19",
    "31",
    "109",
    "233",
    "1229"
  ],
  "discriminant": "69838169048661973147143129899037458432",
  "regulator": "987124779.419637045747458003598609557742373179472540356",
  "points": [
    [
      "104714289",
      "-1071491013909"
    ],
    [
      "36802969281/2209",
      "-7047212709478227/103823"
    ],
    [
      "1296504049/729",
      "-38340101398411/19683"
    ],
    [
      "41899729/36",
      "-132865425881/216"
    ],
    [
      "1022121",
      "-124663377"
    ],
    [
      "1212201",
      "730241553"
    ],
    [
      "170641969/36",
      "2177426755351/216"
    ],
    [
      "1768791249/1024",
      "-60203026900071/32768"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5349: https://elliptic-rank.icarm.cloud/curve/5349. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (3,8,16,30), reduced by rational fourth-power scaling. Reference: \"High rank elliptic curves with torsion group Z/(2Z)\", Math. Comp. 73 (2004), 323–331, doi:10.1090/S0025-5718-03-01547-3. Eight rational points transported through the isogeny and checked exactly. Rank ≥8 follows from the source curve through the rational isogeny. Rational torsion C2.",
  "created_at": "2026-10-21 15:28:46",
  "updated_at": "2026-10-21 15:28:46"
}