{
  "id": 5072,
  "curve_key": "214695835200:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-4472829900",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 78.27746443023872,
  "faltings_height": 4.591362447494718,
  "conductor": "177832953905191200",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "43",
    "79"
  ],
  "discriminant": "5726999184713718944953536000000",
  "regulator": "3715.8930157299186761226525629522604644410599723926",
  "points": [
    [
      "-59850",
      "7301700"
    ],
    [
      "-56880",
      "8389800"
    ],
    [
      "67725",
      "2776725"
    ],
    [
      "105070",
      "26267500"
    ],
    [
      "109494",
      "28687428"
    ],
    [
      "304150",
      "163632700"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5071: https://elliptic-rank.icarm.cloud/curve/5071. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (10,18,36,60), 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. Points transported by the rational 2-isogeny and reduced with PARI/GP. Six rational points checked exactly; PARI/GP returned rank bounds [6,6]. Rational torsion C2.",
  "created_at": "2026-10-21 02:06:14",
  "updated_at": "2026-10-21 02:06:14"
}