{
  "id": 4997,
  "curve_key": "690270632089200:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-14380638168525",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 102.50431457112198,
  "faltings_height": 6.610266625901656,
  "conductor": "264707525291568724864864800",
  "bad_primes": [
    "2",
    "3",
    "5",
    "59",
    "67",
    "223",
    "443",
    "491"
  ],
  "discriminant": "190333157085186499208241948279687021000000",
  "regulator": "330976.58133838815564273062869764363616629902239651",
  "points": [
    [
      "-257280",
      "1919067600"
    ],
    [
      "4407595",
      "4716126650"
    ],
    [
      "14573371",
      "53717445506"
    ],
    [
      "-359465519/1156",
      "82834361210671/39304"
    ],
    [
      "-29364255/16",
      "287720758575/64"
    ],
    [
      "20235948795/5329",
      "149791597544250/389017"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (16,37,58,61), 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. Six rational points checked exactly; PARI/GP returned rank bounds [6,6]. Rational torsion C2.",
  "created_at": "2026-10-21 01:41:57",
  "updated_at": "2026-10-21 01:41:57"
}