{
  "id": 5197,
  "curve_key": "241776:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-5037",
    "0"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 37.18730086996062,
  "faltings_height": 1.1671821508048759,
  "conductor": "811883808",
  "bad_primes": [
    "2",
    "3",
    "23",
    "73"
  ],
  "discriminant": "8178917481792",
  "regulator": "64.00045205127535212964565537438378414468288753",
  "points": [
    [
      "-69",
      "138"
    ],
    [
      "-23",
      "322"
    ],
    [
      "75",
      "210"
    ],
    [
      "121",
      "1078"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (1,12,20,21), 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 by height screening in a bounded tuple search, following the parametrization search 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 09:29:06",
  "updated_at": "2026-10-21 09:29:06"
}