{
  "id": 5082,
  "curve_key": "16607398777200:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-345987474525",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 91.32260826438589,
  "faltings_height": 5.678457767006981,
  "conductor": "17025042848453336743200",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "23",
    "31",
    "37",
    "757"
  ],
  "discriminant": "2650703210467327026940120410141000000",
  "regulator": "77010.68905255920417175690189780661360923432781676245",
  "points": [
    [
      "-572880",
      "100970100"
    ],
    [
      "-494109",
      "224325486"
    ],
    [
      "-143220",
      "215904150"
    ],
    [
      "-17871",
      "78596658"
    ],
    [
      "588225",
      "3529350"
    ],
    [
      "765900",
      "429286950"
    ],
    [
      "946275",
      "721061550"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (12,38,42,52), 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. Seven rational points checked exactly; PARI/GP returned rank bounds [7,7]. Rational torsion C2.",
  "created_at": "2026-10-21 02:20:54",
  "updated_at": "2026-10-21 02:20:54"
}