{
  "id": 275,
  "curve_key": "97655442677167731582136525657:-30972386975508289302598442623271619179309149",
  "ainvs": [
    "1",
    "0",
    "1",
    "-2034488389107661074627844285",
    "35847670110541831966937994064437784692732"
  ],
  "rank_lower_bound": 20,
  "naive_height": 200.28333994112498,
  "faltings_height": 14.572218462706555,
  "conductor": "42943483208607336815574462222443765285847682460232958112909965535488718",
  "bad_primes": [
    "2",
    "11",
    "13",
    "41",
    "33882942493",
    "2222460391457",
    "19721425437778783769",
    "2466004856513281132232797"
  ],
  "discriminant": "-16197498753307130570718466689601294928007257164818990602909253701371655741958401236",
  "regulator": "102030176007090039083.688036283641391460542002868509037467276891445799630022015",
  "points": [
    [
      "-286935581018",
      "-190870148372628414290"
    ],
    [
      "52969417814370",
      "276950216682633411746"
    ],
    [
      "7583485767200",
      "144413558575024721811"
    ],
    [
      "27946486312659",
      "28587472751628447056"
    ],
    [
      "38324958975646",
      "-119028506800841604138"
    ],
    [
      "5466090182467",
      "-157766569909090409868"
    ],
    [
      "953813852774",
      "184141289418161265579"
    ],
    [
      "403282323072",
      "187155717037235338220"
    ],
    [
      "-9329617701204",
      "232414725785122010816"
    ],
    [
      "20514524074244",
      "52388521659913741416"
    ],
    [
      "-667941066879",
      "192889322114541114462"
    ],
    [
      "37221137375463/4",
      "1064989158999437585781/8"
    ],
    [
      "-469358923866320/9",
      "285554907899126306516/27"
    ],
    [
      "32416674872899",
      "62937145652566229704"
    ],
    [
      "-42650906952935",
      "-212212575043297396194"
    ],
    [
      "-663480184290155/16",
      "-14153580123795004605281/64"
    ],
    [
      "228058396114600/9",
      "641761265157468659201/27"
    ],
    [
      "517091678959083/4",
      "-11123125931505983025005/8"
    ],
    [
      "586711235002",
      "186156425539390387690"
    ],
    [
      "-31497237573875",
      "262070200192434671788"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Generalized Mestre/Fermigier quartic family from Mestre parameters u=-3, v=-1/2 (canonical primitive roots [0,113,550,753,868,1058]), specialized at T=10239/176. A native M=6000 Nagao rescore selected the curve; quartic rational-point search to bound 2,000,000 plus an integral-x search to 10^12 found and certified 20 independent points.",
  "created_at": "2026-08-20 16:56:01",
  "updated_at": "2026-08-20 16:56:01"
}