{
  "id": 5087,
  "curve_key": "6261303015552816:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-130443812824017",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 109.1194941234358,
  "faltings_height": 7.161531588594474,
  "conductor": "544498825730149822227584521248",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "29",
    "31",
    "43",
    "59",
    "83",
    "157"
  ],
  "discriminant": "142053005812881430048338645132583263642426432",
  "regulator": "4251937.00515022356226059052829892751674803117553030968",
  "points": [
    [
      "-4657719",
      "22506098208"
    ],
    [
      "-1545033",
      "14065980432"
    ],
    [
      "-119567",
      "3949058876"
    ],
    [
      "11550961",
      "5867888188"
    ],
    [
      "17931516",
      "58537433982"
    ],
    [
      "32180604",
      "170669833314"
    ],
    [
      "-2414150849/441",
      "217196323582832/9261"
    ],
    [
      "322911897/4",
      "5744279735733/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5086: https://elliptic-rank.icarm.cloud/curve/5086. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (3,10,18,27), 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. Points transported by the rational 2-isogeny and reduced with PARI/GP. Eight rational points checked exactly; PARI/GP returned rank bounds [8,8]. Rational torsion C2.",
  "created_at": "2026-10-21 02:27:03",
  "updated_at": "2026-10-21 02:27:03"
}