{
  "id": 5073,
  "curve_key": "515603750256:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-10741744797",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 80.90581314468422,
  "faltings_height": 4.810391507031842,
  "conductor": "3692322601084050278688",
  "bad_primes": [
    "2",
    "3",
    "7",
    "17",
    "29",
    "61",
    "73",
    "233"
  ],
  "discriminant": "79323974178080207281566447972672",
  "regulator": "43689.570846531524737657421443965615487277163118130",
  "points": [
    [
      "106947",
      "8627058"
    ],
    [
      "289153",
      "145154806"
    ],
    [
      "297075",
      "151745910"
    ],
    [
      "-49049063/576",
      "238329397117/13824"
    ],
    [
      "-357189/25",
      "1533769566/125"
    ],
    [
      "-8687/4",
      "38631089/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (6,8,16,24), 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. Six rational points checked exactly; PARI/GP returned rank bounds [6,6]. Rational torsion C2.",
  "created_at": "2026-10-21 02:08:13",
  "updated_at": "2026-10-21 02:08:13"
}