{
  "id": 5339,
  "curve_key": "-12229079794407612864:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "254772495716825268",
    "0"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 131.8510451372811,
  "faltings_height": 9.055827506414916,
  "conductor": "14424227683062166561921285520727072",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "19",
    "23",
    "37",
    "73",
    "181",
    "313",
    "1163"
  ],
  "discriminant": "-1058370187853222867430810579494267837505890767081525248",
  "regulator": "1855029755.7246313527836933035981072792262115198544017801",
  "points": [
    [
      "416848068",
      "13365399604284"
    ],
    [
      "15927451309",
      "2011117286233979"
    ],
    [
      "28630826884/4489",
      "383422407825474116/300763"
    ],
    [
      "54420925636/9",
      "12739627007904412/27"
    ],
    [
      "91505812294/225",
      "44118429327804572/3375"
    ],
    [
      "1038769352838/1681",
      "1367008695615475836/68921"
    ],
    [
      "3705841554688/76729",
      "74895956023591297504/21253933"
    ],
    [
      "5713790662372/12769",
      "20588618167612310348/1442897"
    ],
    [
      "16813493765614/7569",
      "70699886450986997204/658503"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5338: https://elliptic-rank.icarm.cloud/curve/5338. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (3,5,20,27), 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 14:05:52",
  "updated_at": "2026-10-21 14:05:52"
}