{
  "id": 5184,
  "curve_key": "0:-31104",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "36"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    3
  ],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 20.69018341452033,
  "faltings_height": -0.21816213966501039,
  "conductor": "972",
  "bad_primes": [
    "2",
    "3"
  ],
  "discriminant": "-559872",
  "regulator": "0.9997893243787936845790832602940192185333",
  "points": [
    [
      "-3",
      "3"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Rational 3-isogeny partner of curve #5164: https://elliptic-rank.icarm.cloud/curve/5164. Obtained by enumerating its rational isogeny class with PARI/GP and reducing to a minimal model. One rational point recovered with PARI/GP and checked exactly; PARI/GP returned rank bounds [1,1]. Rational torsion C3. Source-attributed isogeny partner.",
  "created_at": "2026-10-21 08:49:30",
  "updated_at": "2026-10-21 08:49:30"
}