{
  "id": 4995,
  "curve_key": "-2485627488144:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "51783906003",
    "0"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 85.62463876176388,
  "faltings_height": 5.203626975121813,
  "conductor": "237701754763660005408",
  "bad_primes": [
    "2",
    "3",
    "19",
    "263",
    "281",
    "647"
  ],
  "discriminant": "-8887188484960118638615404125569728",
  "regulator": "3431.498519585966087965475844373941328218580844",
  "points": [
    [
      "30348",
      "39993606"
    ],
    [
      "243627",
      "164548542"
    ],
    [
      "810123",
      "757386606"
    ],
    [
      "2738907",
      "4548411558"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (6,17,20,31), 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. Selected in a bounded tuple search using a small-prime sieve and height screening, following the search approach described by David Renshaw on https://elliptic-rank.icarm.cloud/curve/4986. Four rational points checked exactly; PARI/GP returned rank bounds [4,4]. Rational torsion C2.",
  "created_at": "2026-10-21 01:37:34",
  "updated_at": "2026-10-21 01:37:34"
}