{
  "id": 5296,
  "curve_key": "1125999025200:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-23458313025",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 83.24907533977894,
  "faltings_height": 5.005663356623068,
  "conductor": "78263815108108039200",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "31",
    "67",
    "71",
    "101"
  ],
  "discriminant": "826171683001525169582656761000000",
  "regulator": "349029.3506231218915646007772607622982071934239689310",
  "points": [
    [
      "-125625",
      "31054500"
    ],
    [
      "-80400",
      "36963900"
    ],
    [
      "-6975",
      "12778200"
    ],
    [
      "-804",
      "4342806"
    ],
    [
      "166495",
      "26639200"
    ],
    [
      "-365295/16",
      "1464572025/64"
    ],
    [
      "-14271/4",
      "73167417/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5295: https://elliptic-rank.icarm.cloud/curve/5295. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (2,6,16,17), 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 12:25:48",
  "updated_at": "2026-10-21 12:25:48"
}