{
  "id": 5182,
  "curve_key": "404266800:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-8422225",
    "0"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 59.452756841998564,
  "faltings_height": 3.0226368151413707,
  "conductor": "90795358656800",
  "bad_primes": [
    "2",
    "5",
    "7",
    "17",
    "19",
    "149"
  ],
  "discriminant": "38234946978163369000000",
  "regulator": "395.1713816261585978395753634062242054643458717",
  "points": [
    [
      "-2831",
      "33972"
    ],
    [
      "-2660",
      "59850"
    ],
    [
      "-1615",
      "96900"
    ],
    [
      "-70775/729",
      "562519700/19683"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (2,5,10,13), followed by a rational 2-isogeny and 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 08:39:49",
  "updated_at": "2026-10-21 08:39:49"
}