{
  "id": 5066,
  "curve_key": "1494296496:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-31131177",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 63.37476408539464,
  "faltings_height": 3.3494707520910434,
  "conductor": "31012805804970528",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "41",
    "173"
  ],
  "discriminant": "1930930293562329973902912",
  "regulator": "1467.57362871770068043300496144600775241768999177",
  "points": [
    [
      "-5453",
      "87248"
    ],
    [
      "-4389",
      "228228"
    ],
    [
      "-4325",
      "231820"
    ],
    [
      "6517",
      "271852"
    ],
    [
      "179949",
      "76298376"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5065: https://elliptic-rank.icarm.cloud/curve/5065. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (1,7,10,14), 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 01:59:38",
  "updated_at": "2026-10-21 01:59:38"
}