{
  "id": 5334,
  "curve_key": "17475352610112658800:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-364069846044013725",
    "0"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 132.92196941935228,
  "faltings_height": 9.145071196587514,
  "conductor": "18851107953566130654892075802791200",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "23",
    "47",
    "79",
    "109",
    "131",
    "907"
  ],
  "discriminant": "3088403986686256718890204332645453727448282749149000000",
  "regulator": "556046291.85714120652792263314928253452663726260812503501",
  "points": [
    [
      "631274721",
      "4662595089306"
    ],
    [
      "832353900",
      "16541785231650"
    ],
    [
      "971131249",
      "23713082838082"
    ],
    [
      "2434797964",
      "116394299270038"
    ],
    [
      "-230688690000/841",
      "217084412763409500/24389"
    ],
    [
      "-9221292135/16",
      "274471760398275/64"
    ],
    [
      "-5942705615/36",
      "1610621789305375/216"
    ],
    [
      "-1817306015/16",
      "404196117326225/64"
    ],
    [
      "45959390625/16",
      "9633012901599375/64"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From the Aguirre–Castañeda–Peral parametrization at tuple (1,5,16,25), reduced by rational fourth-power scaling. This is one endpoint of a rational 2-isogeny pair. 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 13:37:29",
  "updated_at": "2026-10-21 13:37:29"
}