{
  "id": 328,
  "curve_key": "8345460694722019121163957255848401:-763037666912497699130268870309691507317797485432601",
  "ainvs": [
    "1",
    "1",
    "1",
    "-173863764473375398357582442830175",
    "883145447815390783031613032285356595588099614085"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 234.3227837212759,
  "faltings_height": 17.294526867950946,
  "conductor": "43849915595748976027625327568140150988792878346340410934428630268647228784770",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "23",
    "61",
    "73",
    "2191393",
    "4871525053",
    "3391795766524988728488283",
    "2107708103066596881109715329"
  ],
  "discriminant": "-574401154490032448091180309990921523509969094823336020555771703114693561881267196456934604800000",
  "regulator": "215082836065331596042.663713546393845550767010246472599703982535459336787726353",
  "points": [
    [
      "31941998887847240931/25",
      "-180517827928710470478646631686/125"
    ],
    [
      "206258866031062743",
      "-93487086643226687096754002"
    ],
    [
      "771254121484677847/9",
      "-669738464562928802228822734/27"
    ],
    [
      "-5933220306606892893/1849",
      "94342751202953563221961862086/79507"
    ],
    [
      "-1600978306397760897/2401",
      "117577254716661291274191781642/117649"
    ],
    [
      "464778094526026998139/65025",
      "1240061708875631545263726393502/16581375"
    ],
    [
      "313311597703542413061/42025",
      "312436274991260495582176776376/8615125"
    ],
    [
      "3093411392862482313196323/394459321",
      "347429895526098239700399623257167418/7834356574381"
    ],
    [
      "8185285099881883",
      "91793246312288872654658"
    ],
    [
      "15096858470837763",
      "1303514990142403131708178"
    ],
    [
      "10797960552934920996148563/687435961",
      "25665349393729466350838506786680856022/18023883461459"
    ],
    [
      "541041732849712921874763/74839801",
      "41227696227699087914184048091151678/647439118451"
    ],
    [
      "570676175961381813",
      "430992475393457730886552378"
    ],
    [
      "11424309699197275467/529",
      "32648714273828998906473039086/12167"
    ],
    [
      "723652538888165559201641715123/86483322728881",
      "95814719273851855249610555828360250364453018/804263853865733631721"
    ],
    [
      "13540405013375301957/2809",
      "59001940533819441962550391016/148877"
    ],
    [
      "34878168740500992225802147/986148409",
      "193335354761655581913272612311002621766/30968018487827"
    ],
    [
      "2567487415508159083/81",
      "3803342018541561798404623442/729"
    ],
    [
      "8409094814293764983571/1155625",
      "71315186350211886547018194600406/1242296875"
    ],
    [
      "3684580453317449370054662715/757288069729",
      "257261432393715538613612283629233370467870/659009495903779567"
    ]
  ],
  "submitter": "7fff-zip",
  "commentary": "New in this search: Mestre quartic family with roots [0,115,206,234,731,784], T=17595/22. 20 independent rational points certified exactly by Cremona-Brumer quadratic characters; quartic point box [10000000,10000].",
  "created_at": "2026-08-24 19:17:24",
  "updated_at": "2026-08-24 19:17:24"
}