{
  "id": 533,
  "curve_key": "60791401431929557410841497241:-14434228463438685880831369842071968395158461",
  "ainvs": [
    "1",
    "0",
    "1",
    "-1266487529831865779392531193",
    "16706282943794669784408821698768347376056"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 198.83173759797936,
  "faltings_height": 14.494234983282468,
  "conductor": "241154232037315742245497393361765425260101143681401714404719114163883110",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "313187314334176288630516095275020032805326160625197031694440408005043"
  ],
  "discriminant": "9440634675009827659953833972221002806840631527976842381659765887969239103791772500",
  "regulator": "155443454521690292548.251978783544150622523990963507996049669303758391401770483",
  "points": [
    [
      "2255485070205",
      "-117733655455667470018"
    ],
    [
      "23788512122280",
      "-6339477845192470393"
    ],
    [
      "23724977687085",
      "3616766059212129332"
    ],
    [
      "-737235888715",
      "132814089618736199182"
    ],
    [
      "-1273438365140",
      "135340355623518053132"
    ],
    [
      "-265605374360",
      "130547501452529672327"
    ],
    [
      "-386197568460",
      "131131002429369017927"
    ],
    [
      "17229349667985",
      "259477774646323632"
    ],
    [
      "-40423220401330",
      "42997228319011052882"
    ],
    [
      "11926795629895/9",
      "-3310145129730530373476/27"
    ],
    [
      "767377433183815/9",
      "19630108388808896490164/27"
    ],
    [
      "981625649750815/9",
      "29280741825455766472864/27"
    ],
    [
      "7812539722725",
      "-85373555081886647508"
    ],
    [
      "503620295655",
      "126761909857285229112"
    ],
    [
      "-827959599705",
      "133245322551617971632"
    ],
    [
      "44179380581297",
      "216757316807814585598"
    ],
    [
      "-40913945550155",
      "-5945326195157340868"
    ],
    [
      "102758596850215/4",
      "-268298927782570034219/8"
    ],
    [
      "9183698227070695/324",
      "-348989827653634027580351/5832"
    ],
    [
      "917099127054661/25",
      "17505620962585368804676/125"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Generalized Mestre/Fermigier quartic family at integer Mestre parameters (u,v)=(2,6), canonical primitive root sextuple [0,432,707,1426,1606,2075], specialized at T=2564/5 (equivalently roots [1041/16,-517/8,167/8,-385/16,609/16,-565/16] at T=641/20). Selected by a native M=6000 Nagao rescore of a wide-denominator (n<=2000) sieve of the rational q<=3 Mestre families; the 12 family base points plus a quartic-model rational point search to height 1e5 and an integral-x search to 10^12 gave 20 independent points.",
  "created_at": "2026-09-02 19:20:13",
  "updated_at": "2026-09-02 19:20:13"
}