{
  "id": 5244,
  "curve_key": "1336468872816:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-27843101517",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 83.76315624654028,
  "faltings_height": 5.048503432186513,
  "conductor": "205021699725214598688",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "41",
    "79",
    "199"
  ],
  "discriminant": "1381442479670163940363056560346432",
  "regulator": "73703.49747887285088748790095459605135143626251050450",
  "points": [
    [
      "-162503",
      "15275282"
    ],
    [
      "-3927",
      "10453674"
    ],
    [
      "518793",
      "353816826"
    ],
    [
      "-39947061/529",
      "497500697694/12167"
    ],
    [
      "-391919/4",
      "338226097/8"
    ],
    [
      "-269247/4",
      "316903719/8"
    ],
    [
      "2939827/9",
      "4333304998/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (5,8,11,18), 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 following the parametrization search described by David Renshaw on https://elliptic-rank.icarm.cloud/curve/4986. Seven rational points checked exactly; PARI/GP returned rank bounds [7,7]. Rational torsion C2.",
  "created_at": "2026-10-21 10:59:01",
  "updated_at": "2026-10-21 10:59:01"
}