{
  "id": 543,
  "curve_key": "35930893947446918888093359235174197965027136674784224802081:-7146472565549882264761523554425745171595241829022021425759200684344686314043032369127729",
  "ainvs": [
    "1",
    "0",
    "0",
    "-748560290571810810168611650732795790938065347391338016710",
    "8271380284201252621251763373115565776243138253113288642252823365042992603044972259172"
  ],
  "rank_lower_bound": 29,
  "torsion": [],
  "naive_height": 404.58304395595286,
  "faltings_height": 31.65102662842261,
  "conductor": "974577964543442160892570415381135671939306278462543535324631397980273407284075830036683707470545054553959558881958229183929792217811973208902830",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "19",
    "23",
    "31",
    "127",
    "241",
    "147454289",
    "20554377348023",
    "1886568027092676434153747674819284839876889875232293",
    "55475379361618690930805426825153019584420146406248287036257"
  ],
  "discriminant": "-2710786471462749374614993166292988263188121797565799307100057421878289674658661348034237800500607508194038487108944963636095898561841141607117519789597580369102388428800000",
  "regulator": "855753994549180338636678654638509471.993532750149501355044133541558785078092351885135831943387798",
  "points": [
    [
      "12764923916343910128018502444",
      "-892201621382245053856737383957989945960982"
    ],
    [
      "544024912411844929335175670764",
      "-400764692039090584129521311748663221770247702"
    ],
    [
      "20318429794111432649703945388",
      "-1204177091010487294365456382976784591889814"
    ],
    [
      "16036849246742379039129168088",
      "625457593569114636133824303892456860231466"
    ],
    [
      "87791195160313344693665000524",
      "-24883466897594838297601597582021025549118902"
    ],
    [
      "29253966742316885336780461804",
      "3377633540354457744230452977000902919871978"
    ],
    [
      "718932165594491252382810298636/49",
      "-229297733994110398675579724462370189372783866/343"
    ],
    [
      "54222670865503667641072187164",
      "-11273970468846699264482117348660956310428502"
    ],
    [
      "-30531611468201370216070739156",
      "1632542821925833904280282199075711433373418"
    ],
    [
      "-31640343181896987418340764116",
      "529697222543986246862906603827280455425258"
    ],
    [
      "21317907654223796752151274404236/1369",
      "31665715577546034225428530091659245868892371714/50653"
    ],
    [
      "-5862095345745666379209173876",
      "3529598572978841822032080308738291481411178"
    ],
    [
      "246275548529407628813307991564/25",
      "-170168370078468078679308012324155199626821822/125"
    ],
    [
      "10841796261909760707886476124",
      "-1195841187407231779902224629172525315138822"
    ],
    [
      "1228817851199913240439824392716/49",
      "-787451786761089211095937738262123115718291706/343"
    ],
    [
      "117699018018179798292291569656/9",
      "-22887506376673667805917674188581772883000534/27"
    ],
    [
      "14686865856400334005318528684",
      "667376838907779567436158764386428594174058"
    ],
    [
      "835534371623331993177259720636/49",
      "-233924450667146660775487050705828197493844586/343"
    ],
    [
      "16850620560590856531494022124",
      "-665054568332500746262530494302487655140822"
    ],
    [
      "-1180319481326411831956487066",
      "-3025438184992674044313404078396960639976242"
    ],
    [
      "23652656497044410362611162245596/1369",
      "-35660761716886260947025285884337878475319937726/50653"
    ],
    [
      "273134481541166735107720131484",
      "142057431667765465821019752417304659742719658"
    ],
    [
      "-1319951899884441331785093598652/49",
      "-1022616100459927576764849811779798741279119426/343"
    ],
    [
      "13552949976283104399400090924",
      "-784614051421290097428129231806739237606422"
    ],
    [
      "-30208060082372538649437813776",
      "1821611176443968203029651251697875084076298"
    ],
    [
      "157172699302652604246864013744204/10201",
      "-647974542535012363626899961956561768879670739582/1030301"
    ],
    [
      "-28487278521932224930973843156",
      "2545129858954371526289281904377605796509418"
    ],
    [
      "14478482766835875781720999556733904/707281",
      "734799629824145619209353923916710538822891739044918/594823321"
    ],
    [
      "31432761881961468017459908204",
      "3974696689768925914049154262092987973821418"
    ]
  ],
  "submitter": "Mundoamundo",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-09-11 19:08:56"
    }
  ],
  "commentary": "Fiber t = 18909/3310 of a rank-17 elliptic fibration of Elkies' K3 surface (arXiv:2608.25406): the 2-neighbor fibration that also carries wgxli's #391 and #390. Found by a Mestre-Nagao sieve over t = a/b and an iterated 'bootstrap' 2-covering point search (fake 2-descent over random cosets of the growing known lattice); 17 points are specializations of the generic sections, 12 were found on the coverings; the basis shown is LLL-reduced. Search run by Claude (Anthropic) with Seth Lupo, 2026-09-03.",
  "created_at": "2026-09-02 23:15:14",
  "updated_at": "2026-09-11 19:08:56"
}