{
  "id": 5275,
  "curve_key": "218301652800:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-4547951100",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 78.3274310151177,
  "faltings_height": 4.5955263295679645,
  "conductor": "183856526293255200",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "29",
    "31",
    "73"
  ],
  "discriminant": "6020427535182640147829184000000",
  "regulator": "2532.7206347542053005773194962501017961036445736521",
  "points": [
    [
      "-66990",
      "2009700"
    ],
    [
      "71610",
      "6444900"
    ],
    [
      "97650",
      "22068900"
    ],
    [
      "98890",
      "22744700"
    ],
    [
      "134850",
      "42882300"
    ],
    [
      "-148335/4",
      "86775975/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5274: https://elliptic-rank.icarm.cloud/curve/5274. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (4,6,12,13), 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.",
  "created_at": "2026-10-21 11:48:00",
  "updated_at": "2026-10-21 11:48:00"
}