{
  "id": 5075,
  "curve_key": "-2062415001024:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "42966979188",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 85.0646962280439,
  "faltings_height": 5.156965097311815,
  "conductor": "3692322601084050278688",
  "bad_primes": [
    "2",
    "3",
    "7",
    "17",
    "29",
    "61",
    "73",
    "233"
  ],
  "discriminant": "-5076734347397133266020252670251008",
  "regulator": "43689.570846531524737657421443965615487277163118130",
  "points": [
    [
      "142800",
      "95119080"
    ],
    [
      "357189",
      "246817599"
    ],
    [
      "289153/4",
      "472186849/8"
    ],
    [
      "298473/4",
      "481436949/8"
    ],
    [
      "1156612/9",
      "2360645092/27"
    ],
    [
      "6358884/25",
      "20685449652/125"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5073: https://elliptic-rank.icarm.cloud/curve/5073. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (6,8,16,24), 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. Six rational points checked exactly; PARI/GP returned rank bounds [6,6]. Rational torsion C2.",
  "created_at": "2026-10-21 02:12:47",
  "updated_at": "2026-10-21 02:12:47"
}