{
  "id": 5081,
  "curve_key": "65495143619136:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1364482158732",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 95.43899133780513,
  "faltings_height": 6.021489689791919,
  "conductor": "8443589848063214711328",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "41",
    "233",
    "433"
  ],
  "discriminant": "162586154149433815630207689524531146752",
  "regulator": "51174202.82506815966031416536945751521736114734894364",
  "points": [
    [
      "-607563",
      "777648663"
    ],
    [
      "-866",
      "34375004"
    ],
    [
      "1444422",
      "1021121388"
    ],
    [
      "-102670395946800363/869412650929",
      "323744008163371049640103047/810660352217170967"
    ],
    [
      "-884592786/26569",
      "922686899884596/4330747"
    ],
    [
      "1683144177/784",
      "57936800442807/21952"
    ],
    [
      "33274451364/1681",
      "6059110000046796/68921"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5080: https://elliptic-rank.icarm.cloud/curve/5080. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (6,18,20,52), 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. Seven rational points checked exactly; PARI/GP returned rank bounds [7,7]. Rational torsion C2.",
  "created_at": "2026-10-21 02:19:45",
  "updated_at": "2026-10-21 02:19:45"
}