{
  "id": 5280,
  "curve_key": "3703869305136:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-77163943857",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 86.82119744189839,
  "faltings_height": 5.303340198466356,
  "conductor": "527802701967091238688",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "17",
    "19",
    "53",
    "79"
  ],
  "discriminant": "29405138080880625962283976041202752",
  "regulator": "527642.6564401993606535796644834920021614444821781906",
  "points": [
    [
      "-274911",
      "20893236"
    ],
    [
      "-248729",
      "61684792"
    ],
    [
      "299079",
      "60613344"
    ],
    [
      "335559",
      "109045104"
    ],
    [
      "919296",
      "840217392"
    ],
    [
      "16083804",
      "64493860794"
    ],
    [
      "-277508/9",
      "1308866482/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5279: https://elliptic-rank.icarm.cloud/curve/5279. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (1,2,10,16), 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 11:58:45",
  "updated_at": "2026-10-21 11:58:45"
}