{
  "id": 5027,
  "curve_key": "-1328902272:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "27685464",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 63.02285723695493,
  "faltings_height": 3.3201451813877343,
  "conductor": "3065939667581184",
  "bad_primes": [
    "2",
    "3",
    "43",
    "139",
    "193"
  ],
  "discriminant": "-1358111396687853387350016",
  "regulator": "7287.59517704413386824959437652810781658166500324",
  "points": [
    [
      "193",
      "73147"
    ],
    [
      "4632",
      "477096"
    ],
    [
      "9457",
      "1052429"
    ],
    [
      "18528",
      "2621712"
    ],
    [
      "18972672/1849",
      "92872118784/79507"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5001: https://elliptic-rank.icarm.cloud/curve/5001. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (6,8,9,28), 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. Five rational points checked exactly; PARI/GP returned rank bounds [5,5]. Rational torsion C2.",
  "created_at": "2026-10-21 01:48:17",
  "updated_at": "2026-10-21 01:48:17"
}