{
  "id": 5204,
  "curve_key": "2396736:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-49932",
    "0"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 44.0688551090365,
  "faltings_height": 1.7406450040611985,
  "conductor": "554045472",
  "bad_primes": [
    "2",
    "3",
    "19",
    "73"
  ],
  "discriminant": "7967404370276352",
  "regulator": "25.17573887412513549894803819538041957389724948",
  "points": [
    [
      "-219",
      "657"
    ],
    [
      "-171",
      "1881"
    ],
    [
      "-146",
      "2044"
    ],
    [
      "438",
      "7884"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5203: https://elliptic-rank.icarm.cloud/curve/5203. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (1,3,6,10), 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. Four rational points checked exactly; PARI/GP returned rank bounds [4,4]. Rational torsion C2.",
  "created_at": "2026-10-21 09:49:15",
  "updated_at": "2026-10-21 09:49:15"
}