{
  "id": 4031,
  "curve_key": "136046767299328330460048430148048406953799357435557421521:-1668452779531658723705859144009105466887634256593620581213138579447847291626848460569",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2834307652069340217917675628084341811537486613240779615",
    "1931079605939419819104003638663235319373427964008736037026696723399477147538787417"
  ],
  "rank_lower_bound": 30,
  "torsion": [],
  "naive_height": 387.85808905831783,
  "faltings_height": 30.25923843977126,
  "conductor": "36620619861669310619532542906922868058695389054293973367743460649613195853914096997262811694076811652314749863134242643580060715010",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "23",
    "59",
    "61",
    "101",
    "151",
    "1873",
    "104947",
    "219351662577960980356956685810529567803",
    "188451993109847692396423936844736169496573167975969779465712869624947963"
  ],
  "discriminant": "-153751597887697915322829274834511597879651203457094733990941034476431869873217573382545170357622080002977167471608725107175433551583447130594663843611587869900800000",
  "regulator": "93612927982053184023062813185193209.618562528843181783854389970308345183729097981086314473329016925",
  "points": [
    [
      "-30524876398463693829072721354074/20449",
      "155719529593274708859191215264739695422415771491/2924207"
    ],
    [
      "10820724982546288609507538910534/1681",
      "-34488937817711916426145110366794361453708370587/68921"
    ],
    [
      "1024065804416949612358568934",
      "10124766681635268222351121030496435327373"
    ],
    [
      "24580974997697395397540079798006/1369",
      "-121354047866711520860669266524907576227322339911/50653"
    ],
    [
      "1064358287840879568587443974",
      "10960299661355304175108862039823090327213"
    ],
    [
      "9211495509445027177634670428118/2809",
      "-24867757878421861626842076608455403932085417655/148877"
    ],
    [
      "1880934818907908063632399872",
      "-57048406262100642241483364419874249248677"
    ],
    [
      "-1352661636919394520139398906",
      "-57358370129808002805802428075285993328467"
    ],
    [
      "1631161371806940971265782687475414/22201",
      "-65861619814775539202328128281975491136649864325783/3307949"
    ],
    [
      "-894743744892792976302020117778/2809",
      "-7880034166002749130160624546227264841699699143/148877"
    ],
    [
      "1368731499022509230605558758",
      "24817141405000569359377772516396462953101"
    ],
    [
      "-182582571934997751575221242186/121",
      "-70078722993594263372287668350365869379477737/1331"
    ],
    [
      "-1838922659677566911590383318",
      "30406974469839038139121384939785242756565"
    ],
    [
      "549344518577257395604772454",
      "-23234652839520142670438373578312230702707"
    ],
    [
      "2039135094000790984868044235406/2209",
      "1045036029235785746477048489967512159217188379/103823"
    ],
    [
      "193179295888616674460250828429/16",
      "-84124036589658336811366294952572587502747653/64"
    ],
    [
      "943637111089185854172263082",
      "9837902620939839835814016846164638477953"
    ],
    [
      "4046243271353957296121232280025454797276010559542/16501930251578021361721",
      "74973104657986251358032495289349146827232133472483713544239876425364156553/2119835304313559865411499725983981"
    ],
    [
      "-120564284297506675116593642719783137815714780293309925857077688932128986842/144829418278157898675438622683493708579165474369",
      "3358806797300476942762250975138668203916734691580733732084572982927947427963067452002450108842866389828653281555/55116950302198923206767547604659967955695675896506800312047139822322847"
    ],
    [
      "3607775964390015807592873623141430800041756724731068566/4103240781995943036313661449",
      "2864171908486279474117771410414201065157826780308550348906702761112966632902793249/262839422181886541329789223673195158456293"
    ],
    [
      "-996033065381703814915500909517277879195841822614376346340807598893129778/812969912721188335152227295958918846485739201",
      "1383928545647954345293168715032955216609967552683479467925889828616073654464109389481807886192259968095105323/23179908087222803359449045230350796833559765906406192226212416067551"
    ],
    [
      "5142859762326529539712368440072522485516328386554695044578455348899314/3327823612490963426236254224087944770203881",
      "213928444480870410985094775166233886348002092593725168204011366823166375752706806433387493390979876550707/6070723439476022508969004799558713161791291122215247372247280779"
    ],
    [
      "-2687650275003139712501343727743056710364166202195920220250593715953603716/1458605090503809325920009644265352306051230601",
      "1668877087729938198768597190407016752268590017812123610314506642135439888120473749600031324266873874802168977/55706591643387630269677945845431129031046962931179909175733286925349"
    ],
    [
      "264411503658328622039454467974426848951881918086538865966/195405187354240458380308587289",
      "2068500993372418573922348124247623499961010299119167130230932942459672260261026139599/86378196655062680039169481091195878717692163"
    ],
    [
      "3344254876730626620631276228120174791225962860043341967456933804007433996868090625521214/4754632084272329692084896589132628864412393677783050456661401",
      "175175535774556157955973092014975026240404077714543537859061691515162369299535718683569473585183415465502869804160416223257235941567/10367531772533293007564474949442321878591470018621362247776560035023836269553599942905272899"
    ],
    [
      "56553393070619837720991507590770382802258796377596219328492/51962971203563462122783512227401",
      "4360413746686389101874267340040026625390234074975875959130188025099606334336727576198925/374576876287219403312975739123572159240991969851"
    ],
    [
      "-36801795768988748592995225202738837661133832455015622/20832865335706003955886289",
      "3589868750039467823310805647563096227242846254373176428727749803160367940882669/95087517646369041917146157889720597913"
    ],
    [
      "6282909417586422040585662049083525933044101932247640847895805414049/5991366633999915709314657214857088960576",
      "4909093543549884430240006524122949733654343618229825768674392655393216587315570025616721007005740387/463755255990329163930584424369982843553211784495759602573824"
    ],
    [
      "36611399204021864044639646245452221655028643644693976128862704044917913763180513056094138407/28689352430797806621019201730354115418045958940975527574127634596",
      "96250895349925552163304955173451955131114556649501935821938660575351377628665409908007211975544976224920285035693590675557979679140147275/4859382869375931262915833383118409102551321422644719098047991960792598952964089662535222075584856"
    ],
    [
      "116917978602807482325085309982102920515675309991242653590774775499766075180489855295959907463457206680573332894250558486/133053987708530539668204598588524842672427058509684385987798791514885728817544456469098335969",
      "16743460304400840253492770865353705587006660662267400129456373198217241063098598953349955063896563743725510595860743601603487191036770977524148651831793710177461586412389989652749/1534764844802076813029783149915039823982605916231449018439774447272953687561535106657028392958180945441145935508740219962575318894789375953"
    ]
  ],
  "submitter": "Ritik Jain",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-10-05 20:01:59"
    }
  ],
  "commentary": null,
  "created_at": "2026-10-05 19:30:05",
  "updated_at": "2026-10-05 20:01:58"
}