{
  "id": 5065,
  "curve_key": "-5977185984:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "124524708",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 67.53364716875431,
  "faltings_height": 3.696044342371016,
  "conductor": "31012805804970528",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "41",
    "173"
  ],
  "discriminant": "-123579538787989118329786368",
  "regulator": "2935.14725743540136086600992289201550483537998354",
  "points": [
    [
      "3444",
      "685356"
    ],
    [
      "4389",
      "794409"
    ],
    [
      "7749",
      "1195929"
    ],
    [
      "17556",
      "2756292"
    ],
    [
      "548416/49",
      "573506032/343"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (1,7,10,14), 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 01:58:22",
  "updated_at": "2026-10-21 01:58:22"
}