{
  "id": 5064,
  "curve_key": "18826226496:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-392213052",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 70.97555028305999,
  "faltings_height": 3.9828696018964895,
  "conductor": "697646612966688",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "29",
    "41"
  ],
  "discriminant": "3861411626064166924543782912",
  "regulator": "371.144620790039377848490919165777930126176060557",
  "points": [
    [
      "-13398",
      "1688148"
    ],
    [
      "-5166",
      "1374156"
    ],
    [
      "-3654",
      "1176588"
    ],
    [
      "20706",
      "869652"
    ],
    [
      "183106/9",
      "17944388/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5063: https://elliptic-rank.icarm.cloud/curve/5063. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (6,12,27,36), 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. Five rational points checked exactly; PARI/GP returned rank bounds [5,5]. Rational torsion C2.",
  "created_at": "2026-10-21 01:57:02",
  "updated_at": "2026-10-21 01:57:02"
}