{
  "id": 4996,
  "curve_key": "-5007693574224:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "104326949463",
    "0"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 87.72598968179621,
  "faltings_height": 5.378739551791175,
  "conductor": "348291596296171391627808",
  "bad_primes": [
    "2",
    "3",
    "11",
    "19",
    "41",
    "47",
    "79",
    "1093"
  ],
  "discriminant": "-72672399530356541509481413042934208",
  "regulator": "3311.968747149625711307731929242855900701031794",
  "points": [
    [
      "1904769/4",
      "3176519769/8"
    ],
    [
      "2741244/25",
      "14118777222/125"
    ],
    [
      "7459417/4",
      "20676438293/8"
    ],
    [
      "178565596/25",
      "2388582694894/125"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (3,10,18,51), 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 01:40:09",
  "updated_at": "2026-10-21 01:40:09"
}