{
  "id": 5219,
  "curve_key": "117746496:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-2453052",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 55.752133597368726,
  "faltings_height": 2.7142515447555504,
  "conductor": "12034928229408",
  "bad_primes": [
    "2",
    "3",
    "7",
    "19",
    "29",
    "53"
  ],
  "discriminant": "944713752416184102912",
  "regulator": "410.366438305173419075460461185580356147913092998",
  "points": [
    [
      "-1484",
      "19292"
    ],
    [
      "-812",
      "38164"
    ],
    [
      "-318",
      "27348"
    ],
    [
      "6612",
      "522348"
    ],
    [
      "14098",
      "1663564"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5218: https://elliptic-rank.icarm.cloud/curve/5218. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (1,2,9,22), 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. Five rational points checked exactly; PARI/GP returned rank bounds [5,5]. Rational torsion C2.",
  "created_at": "2026-10-21 10:26:05",
  "updated_at": "2026-10-21 10:26:05"
}