This is a list of groups with unproven minimal discriminant for at least one signature.
Number of groups: 103 Missing minimal discriminants: 351
| Not yet proven minimal discriminants of degree 15 | ||||||||||
| G | Name | |G| | 1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 |
|---|---|---|---|---|---|---|---|---|---|---|
| 15T2 | D(15) | 30 | 4947491410771484375 | - | - | - | - | - | - | 1892224296352703538580899969 |
| 15T3 | D(5)[x]3 | 30 | - | 334095024862954369 | - | - | - | - | - | 859597094013128457246001 |
| 15T4 | 5[x]S(3) | 30 | - | - | 35351257235385344 | - | - | - | - | 140998454960622300613 |
| 15T5 | A_5(15) | 60 | - | 23713122135310336 | - | - | - | - | - | 29766469523035740663169 |
| 15T6 | F(5)[1/2]S(3) | 60 | - | 787838463576940... 20 digits | - | - | - | - | - | 897397249918108651776000000 |
| 15T7 | D(5)[x]S(3) | 60 | 69378727128301847 | 19664802801826816 | 405150968993137... 21 digits | - | - | - | - | 2059511496355375228200617 |
| 15T8 | F(5)[x]3 | 60 | - | 1240576436601868288 | - | - | - | - | - | 1730160900125000000000000 |
| 15T9 | [5^2]3 | 75 | - | - | - | - | - | - | - | 112091076863231... 34 digits |
| 15T10 | S_5(15) | 120 | - | 1483978183108890624 | - | - | - | - | - | 342917935808613... 25 digits |
| 15T11 | F(5)[x]S(3) | 120 | 1156440847592456192 | 189863754266000... 21 digits | 205885750000000... 22 digits | - | - | - | - | 11527956194382420421735424 |
| 15T12 | [5^2:2]3 | 150 | - | 929177288598830... 22 digits | - | - | - | - | - | 766139150610351... 31 digits |
| 15T13 | [5^2]S(3) | 150 | - | - | 9599811568837632 | - | - | - | - | 192468056342800... 26 digits |
| 15T14 | 5^2:2[1/2]S(3) | 150 | 196347951889038... 22 digits | - | - | - | - | - | - | 542142253242590... 30 digits |
| 15T15 | 3A_5(15)=[3]A(5)=GL(2,4) | 180 | - | 872411699045053489 | - | - | - | - | - | 542429102709357... 27 digits |
| 15T16 | A(5)[x]3 | 180 | - | 418097075128227... 20 digits | - | - | - | - | - | 23775427618300208865265216 |
| 15T17 | 1/2[5^2:4]S(3) | 300 | - | 217924025062500... 23 digits | - | - | - | - | - | 136202515664062... 34 digits |
| 15T18 | [5^2:2]S(3) | 300 | 1005792029461681407 | 657520280528436... 22 digits | 8144027207463600128 | - | - | - | - | 736067165763683... 31 digits |
| 15T19 | [5^2:4]3 | 300 | - | 8620460479736328125 | - | - | - | - | - | 673137167231445... 31 digits |
| 15T20 | A_6(15) | 360 | - | 189535253532864... 20 digits | - | - | - | - | - | 116217595108466... 29 digits |
| 15T21 | 3S_5(15) | 360 | - | 819758943564295... 22 digits | - | - | - | - | - | 157324731126840... 28 digits |
| 15T22 | S(5)[1/2]S(3) | 360 | - | 4654429023082955776 | - | - | - | - | - | 108740538336869... 28 digits |
| 15T23 | A(5)[x]S(3) | 360 | 957206371560558183 | 640934066430577... 21 digits | 320557557052588... 22 digits | - | - | - | - | 63095343954661026090442701 |
| 15T24 | S(5)[x]3 | 360 | - | 1788527348449625 | - | - | 836457192404894144 | - | - | 585891880179643237473 |
| 15T25 | [5^3]3=5wr3 | 375 | - | - | - | - | - | - | - | 332893714338693... 23 digits |
| 15T26 | [3^4]5 | 405 | - | - | - | - | - | - | - | 374120183433083... 29 digits |
| 15T27 | [5^2:4]S(3) | 600 | 196421600341796875 | 6154112798000000000 | 103907026580810... 21 digits | - | - | - | - | 246164511920000... 26 digits |
| 15T28 | S_6(15) | 720 | - | 31123779291971584 | - | 2975546764864246329 | - | - | - | 123374497805640... 24 digits |
| 15T29 | S(5)[x]S(3) | 720 | 6401597515801839 | 98765528526263521 | 785245957869050... 20 digits | - | 100133149236970... 21 digits | - | - | 555278804074785... 24 digits |
| 15T30 | [5^3:2]3 | 750 | - | 145646455532629401 | - | - | - | - | - | 304492012821002... 28 digits |
| 15T31 | 1/2[5^3:2]S(3) | 750 | 519535132904052... 21 digits | - | - | - | - | - | - | 211174818907795... 32 digits |
| 15T32 | [5^3]S(3) | 750 | - | - | 8431282707797071 | - | - | - | - | 151918500761535... 21 digits |
| 15T33 | [3^4:2]5 | 810 | - | - | 450330169037305... 20 digits | - | - | - | - | 138622929316925... 27 digits |
| 15T34 | [3^4]D(5) | 810 | - | 129186640449535761 | - | - | - | - | - | 952890326364184... 26 digits |
| 15T35 | 1/2[3^4:2]D(5) | 810 | 151702388076465... 21 digits | - | - | - | - | - | - | 102971444303329... 32 digits |
| 15T36 | [3^5]5=3wr5 | 1215 | - | - | - | - | - | - | - | 587687199391427... 22 digits |
| 15T37 | 1/2[5^3:4]S(3) | 1500 | - | 139471376040000... 23 digits | - | - | - | - | - | 257592720731513... 31 digits |
| 15T38 | [5^3:4]3 | 1500 | - | 118310588512598... 21 digits | - | - | - | - | - | 430807787028125... 27 digits |
| 15T39 | [1/2.D(5)^3]3 | 1500 | - | - | - | 227976056096178... 20 digits | - | - | - | 132159059532406... 35 digits |
| 15T40 | [5^3:2]S(3) | 1500 | 109880121698811904 | 2368988465121722368 | 136193017880000... 21 digits | - | - | - | - | 163182013910625... 36 digits |
| 15T41 | [3^4]F(5) | 1620 | - | 459433731019393... 20 digits | - | - | - | - | - | 754028656648743... 30 digits |
| 15T42 | 1/2[3^4:2]F(5) | 1620 | - | 781037342732968... 21 digits | - | - | - | - | - | 683861807900390... 30 digits |
| 15T43 | [3^4:2]D(5) | 1620 | 154669958288795403 | 3401914865171108373 | 736546275301738... 21 digits | - | - | - | - | 243477988065890... 28 digits |
| 15T44 | [3^5:2]5 | 2430 | - | - | 154972454814106259 | - | - | - | - | 262047125362808... 24 digits |
| 15T45 | 1/2[3^5:2]D(5) | 2430 | 361741573588593575 | - | - | - | - | - | - | 312430954286150... 27 digits |
| 15T46 | [3^5]D(5)=3wrD(5) | 2430 | - | 2432060458605625 | - | - | - | - | - | 148678884286623... 23 digits |
| 15T47 | A_7(15) | 2520 | - | 625987024006096... 22 digits | - | - | - | - | - | 369796439129108... 33 digits |
| 15T48 | 1/2[D(5)^3]S(3) | 3000 | 161587299012694487 | - | - | 505382051812842... 23 digits | - | - | - | 682393412538497... 32 digits |
| 15T49 | [5^3:4]S(3) | 3000 | 182790400000000... 20 digits | 554751656000000... 20 digits | 913302135000000... 23 digits | - | - | - | - | 346719785000000... 27 digits |
| 15T50 | [D(5)^3]3=D(5)wr3 | 3000 | - | 2581408254768721 | - | 96478675843767889 | - | 8132734453956272209 | - | 226634442904047... 21 digits |
| 15T51 | [1/2.D(5)^3]S(3) | 3000 | - | - | 6436343000000000000 | 173359892500000... 20 digits | - | - | - | 178563308551866... 31 digits |
| 15T52 | [3^4:2]F(5) | 3240 | 137830119305818... 21 digits | 398886109930416... 23 digits | 228937203112700... 22 digits | - | - | - | - | 202872567701544... 32 digits |
| 15T53 | [3^4]A(5) | 4860 | - | 57352136505929721 | - | - | - | - | - | 913210082278087... 26 digits |
| 15T54 | 1/2[3^5:2]F(5) | 4860 | - | 107616802500000... 24 digits | - | - | - | - | - | 892702567137409... 30 digits |
| 15T55 | [3^5:2]D(5) | 4860 | 276668772447526875 | 182470557089312... 20 digits | 127862957995645... 22 digits | - | - | - | - | 198094518365361... 30 digits |
| 15T56 | [3^5]F(5)=3wrF(5) | 4860 | - | 59463924292145152 | - | - | - | - | - | 141523503415447... 26 digits |
| 15T57 | [1/4.F(5)^3]3 | 6000 | - | - | - | 903469412181606... 24 digits | - | - | - | 220573586958400... 33 digits |
| 15T58 | 1/2[D(5)^3:2]S(3) | 6000 | - | 9725690310044041216 | - | 124822189039431... 24 digits | - | 851265722900390... 28 digits | - | 479469741926171... 25 digits |
| 15T59 | [D(5)^3:2]3 | 6000 | - | 784139153615644... 20 digits | - | 362870904780330... 21 digits | - | 145685782107543... 22 digits | - | 299209118060166... 30 digits |
| 15T60 | [D(5)^3]S(3)=D(5)wrS(3) | 6000 | 670556550881207 | 10416123605373952 | 27007279664331047 | 253380093937865728 | - | 401914774208119... 20 digits | - | 917410707461700... 22 digits |
| 15T61 | [3^4:2]A(5) | 9720 | 103201735683797... 20 digits | 110821805645000... 22 digits | 930720339686697... 22 digits | - | - | - | - | 343742359211512... 30 digits |
| 15T62 | 1/2[3^4:2]S(5) | 9720 | - | 103399430059674... 20 digits | - | - | - | - | - | 583568207034724... 29 digits |
| 15T63 | [3^4]S(5) | 9720 | - | 2382961487859009 | - | - | 253693722674384... 21 digits | - | - | 582313495113950... 22 digits |
| 15T64 | [3^5:2]F(5) | 9720 | 833787141479640... 20 digits | 436594581987750... 22 digits | 572343007781751... 23 digits | - | - | - | - | 228072762463409... 33 digits |
| 15T65 | 1/2[1/2.F(5)^3]S(3) | 12000 | 395185576262579... 24 digits | - | - | 114398748855746... 32 digits | - | - | - | 310762662547542... 36 digits |
| 15T66 | [1/4.F(5)^3]S(3) | 12000 | - | - | 965054558925639... 22 digits | 112128022503912... 23 digits | - | - | - | 255557069260828... 30 digits |
| 15T67 | [1/2.F(5)^3]3 | 12000 | - | 903469412181606... 24 digits | - | 206869311984658... 27 digits | - | 220573586958400... 33 digits | - | 225867353045401... 26 digits |
| 15T68 | [D(5)^3:2]S(3) | 12000 | 161414428000000... 21 digits | 234382574660000... 24 digits | 709081977233886... 20 digits | 221900662400000... 23 digits | - | 192188535201721... 23 digits | - | 333197713385000... 26 digits |
| 15T69 | [3^5]A(5)=3wrA(5) | 14580 | - | 365798538164160... 20 digits | - | - | - | - | - | 181632093011523... 26 digits |
| 15T70 | [3^4:2]S(5) | 19440 | 59770508839234803 | 1317156265515729717 | 108999598596997... 20 digits | - | 703191532627148... 24 digits | - | - | 835311132168102... 28 digits |
| 15T71 | [1/2.S(3)^5]5 | 19440 | - | - | - | 3069762702266721241 | - | 578885922392385... 25 digits | - | 592779184529802... 28 digits |
| 15T72 | L(15)=A_8(15)=PSL(4,2) | 20160 | - | 443714161909669... 21 digits | - | 236516274161580... 24 digits | - | - | - | 633279463729648... 33 digits |
| 15T73 | 1/2[F(5)^3]S(3) | 24000 | - | 140499178156840... 30 digits | - | 224798685050944... 29 digits | - | 134590775844589... 33 digits | - | 359677896081510... 26 digits |
| 15T74 | [1/2.F(5)^3]S(3) | 24000 | 392911832307960... 21 digits | 101454152380883... 22 digits | 161343104737280... 22 digits | 299581181938889... 28 digits | - | 234038499271148... 29 digits | - | 287932475391560... 33 digits |
| 15T75 | [F(5)^3]3=F(5)wr3 | 24000 | - | 679665130414960... 21 digits | - | 312666020497616... 23 digits | - | 779332668243737... 26 digits | - | 141977890843583... 35 digits |
| 15T76 | [3^5:2]A(5) | 29160 | 117553227052325... 21 digits | 160026687351380... 21 digits | 108752635551363... 25 digits | - | - | - | - | 188613969258415... 33 digits |
| 15T77 | 1/2[3^5:2]S(5) | 29160 | - | 7086046715229147136 | - | - | - | - | - | 300557416625711... 31 digits |
| 15T78 | [3^5]S(5)=3wrS(5) | 29160 | - | 2220941493807129 | - | - | 350591147075913... 20 digits | - | - | 259278094725477... 23 digits |
| 15T79 | 1/2[S(3)^5]D(5) | 38880 | 13999649650909911 | - | - | 121545290697941... 22 digits | - | 164071803765951... 25 digits | - | 256072833895329... 27 digits |
| 15T80 | [1/2.S(3)^5]D(5) | 38880 | - | 384868350609175... 23 digits | - | 161082670408490... 25 digits | - | 198867494331469... 23 digits | - | 991906868948850... 25 digits |
| 15T81 | [S(3)^5]5=S(3)wr5 | 38880 | - | - | 2408991714975128459 | 147760346404401401 | 202000015135095... 20 digits | 461138093094201... 23 digits | 150447757952202... 24 digits | 567303557201160... 24 digits |
| 15T82 | [F(5)^3]S(3)=F(5)wrS(3) | 48000 | 830788835847757... 20 digits | 291317936726763... 25 digits | 126022722858222... 28 digits | 692727712675020... 24 digits | - | 213282122419725... 29 digits | - | 140538189189338... 31 digits |
| 15T83 | [3^5:2]S(5) | 58320 | 70331165071024203 | 380658160734045... 21 digits | 104211256684780... 22 digits | - | 720068129410199... 27 digits | - | - | 493183845957892... 28 digits |
| 15T84 | 1/2[S(3)^5]F(5) | 77760 | - | 688747536000000... 25 digits | - | 458457010314970... 23 digits | - | 303737663376000... 28 digits | - | 114288073113600... 31 digits |
| 15T85 | [1/2.S(3)^5]F(5) | 77760 | - | 387717298852364... 26 digits | - | 550321837470337... 22 digits | - | 934173632812500... 25 digits | - | 193031336102078... 33 digits |
| 15T86 | [S(3)^5]D(5)=S(3)wrD(5) | 77760 | 1122105536533571 | 5410098952840429 | 279341994781103... 23 digits | 144581305892563... 22 digits | 356254943672084... 21 digits | 622037272329206... 22 digits | 295436894871030... 23 digits | 710553557246339... 26 digits |
| 15T87 | [S(3)^5]F(5)=S(3)wrF(5) | 155520 | 274453679358997... 21 digits | 166343586501147... 23 digits | 128501973188750... 26 digits | 314181654500000... 24 digits | 364927455144581... 23 digits | 139318181065000... 26 digits | 310299858703186... 28 digits | 614058946070141... 29 digits |
| 15T88 | [1/2.S(3)^5]A(5) | 233280 | - | 583380745524050... 22 digits | - | 101687772449293... 23 digits | - | 807743129811840... 23 digits | - | 152368073080067... 31 digits |
| 15T89 | 1/2[S(3)^5]S(5) | 466560 | - | 111471392739427... 20 digits | - | 441597411748251... 20 digits | - | 119924098235139... 28 digits | - | 290186943867867... 30 digits |
| 15T90 | [S(3)^5]A(5)=S(3)wrA(5) | 466560 | 314528308881522688 | 3499598836464091136 | 140647909796763... 22 digits | 325400871837740... 23 digits | 505923448739520... 23 digits | 133510178000013... 26 digits | 274828031021817... 25 digits | 845951611095768... 29 digits |
| 15T91 | [1/2.S(3)^5]S(5) | 466560 | - | 305030326745602... 22 digits | 9141237275830859375 | 209272218438203... 22 digits | 327750627860810... 24 digits | 136337442323395... 24 digits | - | 334835549501125... 29 digits |
| 15T92 | [A(5)^3]3=A(5)wr3 | 648000 | - | 252349919319202929 | - | 1646941276323745801 | - | 587722035070506... 42 digits | - | 178142275842344... 23 digits |
| 15T93 | [S(3)^5]S(5)=S(3)wrS(5) | 933120 | 460265293502503 | 3813614073053089 | 58630207945645763 | 134876801588810... 22 digits | 3534005780678716416 | 143609813305490... 25 digits | 102583876287357... 23 digits | 428215667734040... 27 digits |
| 15T94 | 1/2[A(5)^3:2]S(3) | 1296000 | - | 5282782892042358784 | - | 580865457092657... 20 digits | - | 473831966523245... 53 digits | - | 762858540877421... 54 digits |
| 15T95 | [A(5)^3:2]3 | 1296000 | - | 107779860863185189 | - | 3883228524698760125 | 181546548947299... 20 digits | 132136506772165... 46 digits | - | 534163649148864... 54 digits |
| 15T96 | [A(5)^3]S(3)=A(5)wrS(3) | 1296000 | 4025865561167751863 | 3713859004905029632 | 1454383595408929007 | 247751231080317... 20 digits | - | 469656378849340... 28 digits | - | 483807747971682... 26 digits |
| 15T97 | [A(5)^3:2]S(3) | 2592000 | 205962976000000... 22 digits | 480537996567076800 | 166856721405397... 20 digits | 668987701906811... 20 digits | 306142271505832... 20 digits | 634938494714215... 25 digits | - | 248398977558713... 48 digits |
| 15T98 | [1/2.S(5)^3]3 | 2592000 | - | 80801923229617681 | - | 178799850111319969 | - | 602698457701977... 21 digits | - | 981509775960771... 23 digits |
| 15T99 | 1/2[S(5)^3]S(3) | 5184000 | - | 1581785703182128129 | - | 102170171470813... 20 digits | - | 865969921490120... 23 digits | - | 125010533193732... 25 digits |
| 15T100 | [1/2.S(5)^3]S(3) | 5184000 | 154679035105415447 | 873831601003773952 | 200513382366914087 | 6095360892180812800 | - | 173715115340862... 22 digits | - | 562187237772555... 25 digits |
| 15T101 | [S(5)^3]3=S(5)wr3 | 5184000 | - | 7920582932096001 | 40666880000801579 | 98150379056062837 | 3851821975703251991 | 255930699223417... 20 digits | 261043825156182... 22 digits | 205098706621069... 22 digits |
| 15T102 | [S(5)^3]S(3)=S(5)wrS(3) | 10368000 | 462697556960267 | 3979171169409313 | 19369191564087103 | 118657710224087... 20 digits | 103955176521036... 22 digits | 838887404002209... 20 digits | 359303884002985... 23 digits | 776333434608080... 22 digits |
| 15T103 | A(15) | 653837184000 | - | 7640669135883265024 | - | 239350355667544... 36 digits | - | 353770618814061... 72 digits | - | 858548560766890... 99 digits |
| 15T104 | S(15) | 1307674368000 | 426781883555301359 | 6653718481802353153 | 836502653153567... 22 digits | 133311792725173... 23 digits | 893591792459039... 24 digits | 475252033381120... 45 digits | 315651711121163... 46 digits | 545746788015105... 31 digits |
6 | 1,24 ms