{
  "id": 5085,
  "curve_key": "4269984039216:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-88958000817",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 87.24789361582071,
  "faltings_height": 5.338898212959883,
  "conductor": "3126331223449826239008",
  "bad_primes": [
    "2",
    "3",
    "7",
    "19",
    "41",
    "257",
    "2351"
  ],
  "discriminant": "45054172435837684844765435605664832",
  "regulator": "1115582.2539894042433734991027034960012189421065599",
  "points": [
    [
      "-8442441/121",
      "101950917516/1331"
    ],
    [
      "-147231/16",
      "1830228561/64"
    ],
    [
      "48649329/100",
      "268074019233/1000"
    ],
    [
      "48649329/121",
      "227549128176/1331"
    ],
    [
      "5194667241/3721",
      "365756185298988/226981"
    ],
    [
      "385351335009/913936",
      "169084483310727279/873722816"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5084: https://elliptic-rank.icarm.cloud/curve/5084. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (1,6,17,45), 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. Points transported by the rational 2-isogeny and reduced with PARI/GP. Six rational points checked exactly; PARI/GP returned rank bounds [6,6]. Rational torsion C2.",
  "created_at": "2026-10-21 02:24:27",
  "updated_at": "2026-10-21 02:24:27"
}