{
  "id": 6201,
  "curve_key": "17337696:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-361202",
    "0"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 50.00518094554827,
  "faltings_height": 2.2353388237705127,
  "conductor": "8349880627456",
  "bad_primes": [
    "2",
    "313",
    "577"
  ],
  "discriminant": "3015993582398362112",
  "regulator": "2804.81643166821392315040659285281353775372877246",
  "points": [
    [
      "-577",
      "4039"
    ],
    [
      "-313",
      "9077"
    ],
    [
      "-1",
      "601"
    ],
    [
      "-5000/9",
      "145900/27"
    ],
    [
      "2817/4",
      "77937/8"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained from my specialization at (u,v)=(7,1) of the family in Yasutsugu Fujita and Nobuhiro Terai, On the Rank of the Elliptic Curve y^2 = x^3 - nx (2012), Theorem 3.3: https://www.m-hikari.com/ija/ija-2012/ija-17-20-2012/teraiIJA17-20-2012.pdf . Here n=u^8+6*u^4*v^4+25*v^8=5779232 and the source equation is y^2=x^3-n*x. The three source sections seeded my point search, followed by the minimal-model change [u,r,s,t]=[2,0,0,0]. PARI/GP returned rank bounds [5,5]. All five listed rational points were checked exactly on the displayed global minimal model and independently certified. The rational torsion subgroup is Z/2Z.",
  "created_at": "2026-10-30 16:36:39",
  "updated_at": "2026-10-30 16:36:39"
}