{
  "id": 5245,
  "curve_key": "-5345875491264:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "111372406068",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 87.92203932989995,
  "faltings_height": 5.395077022466486,
  "conductor": "205021699725214598688",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "41",
    "79",
    "199"
  ],
  "discriminant": "-88412318698890492183235619862171648",
  "regulator": "147406.9949577457017749758019091921027028725250210090",
  "points": [
    [
      "29766",
      "57805572"
    ],
    [
      "88806",
      "102912132"
    ],
    [
      "111078",
      "117224316"
    ],
    [
      "337348",
      "275613316"
    ],
    [
      "407950",
      "336640340"
    ],
    [
      "1974478/9",
      "5050714724/27"
    ],
    [
      "2108425/4",
      "3623539205/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5244: https://elliptic-rank.icarm.cloud/curve/5244. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (5,8,11,18), 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. Seven rational points checked exactly; PARI/GP returned rank bounds [7,7]. Rational torsion C2.",
  "created_at": "2026-10-21 11:00:21",
  "updated_at": "2026-10-21 11:00:21"
}