{
  "id": 5338,
  "curve_key": "3057269948601903216:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-63693123929206317",
    "0"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 127.69216205392142,
  "faltings_height": 8.709253916134942,
  "conductor": "14424227683062166561921285520727072",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "19",
    "23",
    "37",
    "73",
    "181",
    "313",
    "1163"
  ],
  "discriminant": "16537034185206607303606415304597934961029543235648832",
  "regulator": "103057208.65136840848798296131100595995701175110302232112",
  "points": [
    [
      "-245250837",
      "932443682274"
    ],
    [
      "-83880212",
      "2180004769774"
    ],
    [
      "337319787",
      "4110578924382"
    ],
    [
      "457908633",
      "8176111278426"
    ],
    [
      "551858619",
      "11528998378794"
    ],
    [
      "560225241",
      "11838306309318"
    ],
    [
      "-492489450752/4761",
      "769139335935573616/328509"
    ],
    [
      "-18681091061/81",
      "1134577384498774/729"
    ],
    [
      "23825361049/36",
      "3399664593442859/216"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny endpoint from the Aguirre–Castañeda–Peral parametrization at tuple (3,5,20,27), 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 14:00:27",
  "updated_at": "2026-10-21 14:00:27"
}