{
  "id": 5194,
  "curve_key": "50160:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1045",
    "0"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 32.468919525920406,
  "faltings_height": 0.773983705468191,
  "conductor": "34944800",
  "bad_primes": [
    "2",
    "5",
    "11",
    "19"
  ],
  "discriminant": "73034632000",
  "regulator": "16.727772930469645030824853662433559580558195",
  "points": [
    [
      "-19",
      "114"
    ],
    [
      "44",
      "198"
    ],
    [
      "125",
      "1350"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 2-isogeny partner of curve #5193: https://elliptic-rank.icarm.cloud/curve/5193. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (1,4,8,13), 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. Three rational points checked exactly; PARI/GP returned rank bounds [3,3]. Rational torsion C2.",
  "created_at": "2026-10-21 09:24:08",
  "updated_at": "2026-10-21 09:24:08"
}