{
  "id": 5060,
  "curve_key": "-115263120:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "2401315",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 55.68818421852361,
  "faltings_height": 2.7089224298517913,
  "conductor": "184522039335200",
  "bad_primes": [
    "2",
    "5",
    "7",
    "19",
    "23",
    "157"
  ],
  "discriminant": "-886191081772411576000",
  "regulator": "1857.63187806724715475294961037080499089023565730",
  "points": [
    [
      "35",
      "9170"
    ],
    [
      "785",
      "48670"
    ],
    [
      "9891",
      "995694"
    ],
    [
      "785/4",
      "175055/8"
    ],
    [
      "1099/9",
      "463778/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5049: https://elliptic-rank.icarm.cloud/curve/5049. 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. Points transported by the rational 2-isogeny and reduced with PARI/GP. Five rational points checked exactly; PARI/GP returned rank bounds [5,5]. Rational torsion C2.",
  "created_at": "2026-10-21 01:51:12",
  "updated_at": "2026-10-21 01:51:12"
}