{
  "id": 5234,
  "curve_key": "-76436627904:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "1592429748",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 75.17918352317912,
  "faltings_height": 4.333172371906417,
  "conductor": "5071665004630687008",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "19",
    "23",
    "47",
    "71"
  ],
  "discriminant": "-258440647208462839846922047488",
  "regulator": "13187.890026600013655006887129445329183219379843058",
  "points": [
    [
      "6486",
      "3255972"
    ],
    [
      "6916",
      "3368092"
    ],
    [
      "32292",
      "9224748"
    ],
    [
      "127374",
      "47637876"
    ],
    [
      "1146366",
      "1228140108"
    ],
    [
      "245518/9",
      "215564804/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5233: https://elliptic-rank.icarm.cloud/curve/5233. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (1,12,16,17), 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. Six rational points checked exactly; PARI/GP returned rank bounds [6,6]. Rational torsion C2.",
  "created_at": "2026-10-21 10:46:01",
  "updated_at": "2026-10-21 10:46:01"
}