{
  "id": 5190,
  "curve_key": "368256:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-7672",
    "0"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 38.44960088241349,
  "faltings_height": 1.2723738185092817,
  "conductor": "235438336",
  "bad_primes": [
    "2",
    "7",
    "137"
  ],
  "discriminant": "28900526620672",
  "regulator": "102.8182771564712004478702758274278306467296658",
  "points": [
    [
      "-63",
      "483"
    ],
    [
      "-56",
      "504"
    ],
    [
      "-7",
      "231"
    ],
    [
      "-343/4",
      "1323/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5189: https://elliptic-rank.icarm.cloud/curve/5189. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (1,2,10,13), 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 09:12:55",
  "updated_at": "2026-10-21 09:12:55"
}