{
  "id": 5332,
  "curve_key": "191254993776:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-3984479037",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 77.93062026167767,
  "faltings_height": 4.562458766781296,
  "conductor": "56448260253484257312",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "23",
    "59",
    "223"
  ],
  "discriminant": "4048504373792309930445203433792",
  "regulator": "1542095.772995567599239786680588595186744462816762023",
  "points": [
    [
      "-22077",
      "8786646"
    ],
    [
      "-9812",
      "6176654"
    ],
    [
      "-6608",
      "5103028"
    ],
    [
      "-413",
      "1282778"
    ],
    [
      "124609",
      "37925614"
    ],
    [
      "-3457278272007/54804409",
      "225455428213522794/405717039827"
    ],
    [
      "9117801/25",
      "27116340174/125"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogenous endpoint of the Aguirre–Castañeda–Peral parametrization at tuple (1,8,23,25), 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 13:30:07",
  "updated_at": "2026-10-21 13:30:07"
}