{
  "id": 5286,
  "curve_key": "786735936:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-16390332",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 61.45020965302968,
  "faltings_height": 3.1890912160606306,
  "conductor": "59698440682272",
  "bad_primes": [
    "2",
    "3",
    "7",
    "193",
    "337"
  ],
  "discriminant": "281801451647446443159552",
  "regulator": "1741.3104989998206916926497559155594203886199152284",
  "points": [
    [
      "-4044",
      "12132"
    ],
    [
      "-2702",
      "156716"
    ],
    [
      "-1158",
      "132012"
    ],
    [
      "7077",
      "488313"
    ],
    [
      "8106",
      "632268"
    ],
    [
      "-12159/4",
      "1179423/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5285: https://elliptic-rank.icarm.cloud/curve/5285. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (5,6,17,18), 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 12:11:31",
  "updated_at": "2026-10-21 12:11:31"
}