{
  "id": 5314,
  "curve_key": "4848814656:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-101016972",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 66.90600033360094,
  "faltings_height": 3.6437404394415682,
  "conductor": "2267650807121952",
  "bad_primes": [
    "2",
    "3",
    "7",
    "31",
    "67",
    "193"
  ],
  "discriminant": "65972510809578900221571072",
  "regulator": "2499.2470058419056743172315475988093254614120241403",
  "points": [
    [
      "-10050",
      "12060"
    ],
    [
      "-8106",
      "534996"
    ],
    [
      "-5628",
      "624708"
    ],
    [
      "10854",
      "426924"
    ],
    [
      "24318",
      "3453156"
    ],
    [
      "-77586/25",
      "66568788/125"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5312: https://elliptic-rank.icarm.cloud/curve/5312. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (6,11,18,22), 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.",
  "created_at": "2026-10-21 13:04:19",
  "updated_at": "2026-10-21 13:04:19"
}