{
  "id": 5077,
  "curve_key": "-6240447854784:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "130009330308",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 88.38621920200328,
  "faltings_height": 5.433758678475097,
  "conductor": "33804851934269294749728",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "19",
    "37",
    "47",
    "2293"
  ],
  "discriminant": "-140638277156334382263667127844999168",
  "regulator": "82561.829260471842802137609604693770245238167730071",
  "points": [
    [
      "15466",
      "44882332"
    ],
    [
      "285714",
      "245904516"
    ],
    [
      "958474",
      "1002563804"
    ],
    [
      "1967394",
      "2805503844"
    ],
    [
      "1967394/49",
      "24934751556/343"
    ],
    [
      "42498214356/776161",
      "58354589081537268/683797841"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5076: https://elliptic-rank.icarm.cloud/curve/5076. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (3,4,31,60), 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 02:14:45",
  "updated_at": "2026-10-21 02:14:45"
}