{
  "id": 5049,
  "curve_key": "461052480:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-9605260",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 59.84706730188328,
  "faltings_height": 3.0554960201317636,
  "conductor": "184522039335200",
  "bad_primes": [
    "2",
    "5",
    "7",
    "19",
    "23",
    "157"
  ],
  "discriminant": "56716229233434340864000",
  "regulator": "928.815939033623577376474805185402495445117828652",
  "points": [
    [
      "-3059",
      "27531"
    ],
    [
      "-1610",
      "106260"
    ],
    [
      "5796",
      "372876"
    ],
    [
      "30590",
      "5322660"
    ],
    [
      "-1610/9",
      "1117340/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (2,3,14,24), 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. Five rational points checked exactly; PARI/GP returned rank bounds [5,5]. Rational torsion C2.",
  "created_at": "2026-10-21 01:49:54",
  "updated_at": "2026-10-21 01:49:54"
}