{
  "id": 6363,
  "curve_key": "201606060824242104384:-2862565125960465557611229598048",
  "ainvs": [
    "0",
    "0",
    "0",
    "-4200126267171710508",
    "3313154080972761062050034257"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    6
  ],
  "family": null,
  "families": [],
  "naive_height": 140.25854181975134,
  "faltings_height": 9.02581104735247,
  "conductor": "860763043294883820",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "37",
    "73",
    "523",
    "619",
    "3163"
  ],
  "discriminant": "52297261797930354294337399597878680873152491600",
  "regulator": "104643.91811823517134722564354998253545918609202268",
  "points": [
    [
      "1182889626",
      "20500796225"
    ],
    [
      "1185450174",
      "132094750417"
    ],
    [
      "6342704388",
      "481496990019185"
    ],
    [
      "199984946643/169",
      "14282740147844/2197"
    ],
    [
      "2020843856366/1681",
      "77954896124639625/68921"
    ],
    [
      "9405865960046/7921",
      "177590280533600025/704969"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Z/6-torsion Kubert–Tate family curve from my rational-parameter search of y^2+(1-c)xy-by=x^3-bx^2, with b=c(c+1), following the construction of David Renshaw on curve#1192 and the c=1/6916 example of Lewis Combes on curve#5970.\r\n\r\nHere c=-511/120705. Clearing denominators gives the integral model [121216,61419134,7413596569470,0,0], which reduces to the displayed global minimal model.\r\n\r\nThe completed rank-6 batch identified this specialization. A separate rank computation on the minimal model returned bounds [6,6] and the six displayed rational points. All six points were checked exactly on this model. The minimal discriminant was fully factored and every listed bad-reduction prime proved prime.",
  "created_at": "2026-11-01 14:23:16",
  "updated_at": "2026-11-01 14:23:16"
}