{
  "id": 5097,
  "curve_key": "9356256:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-194922",
    "0"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 48.1546673052973,
  "faltings_height": 2.081129353749599,
  "conductor": "5513953536",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "17"
  ],
  "discriminant": "473982765354588672",
  "regulator": "15.647003410738048702541540154220151114820135",
  "points": [
    [
      "-441",
      "441"
    ],
    [
      "-273",
      "5733"
    ],
    [
      "4641/4",
      "292383/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5096: https://elliptic-rank.icarm.cloud/curve/5096. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (20,28,30,38), 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. Three rational points checked exactly; PARI/GP returned rank bounds [3,3]. Rational torsion C2.",
  "created_at": "2026-10-21 02:42:48",
  "updated_at": "2026-10-21 02:42:48"
}