Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of 129)

Label	Polynomial	Discriminant	Galois group	Class group
7.7.594823321.1	x^7 - x^6 - 12x^5 + 7x^4 + 28x^3 - 14x^2 - 9x - 1	\( 29^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.6321363049.1	x^7 - x^6 - 18x^5 + 35x^4 + 38x^3 - 104x^2 + 7x + 49	\( 43^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.13841287201.1	x^7 - 21x^5 - 21x^4 + 91x^3 + 112x^2 - 84x - 97	\( 7^{12} \)	$C_7$ (as 7T1)	Trivial
7.7.128100283921.1	x^7 - x^6 - 30x^5 - 3x^4 + 254x^3 + 246x^2 - 245x - 137	\( 71^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.2081951752609.1	x^7 - x^6 - 48x^5 - 37x^4 + 312x^3 + 12x^2 - 49x + 1	\( 113^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.4195872914689.1	x^7 - x^6 - 54x^5 + 31x^4 + 558x^3 + 32x^2 - 1713x - 1121	\( 127^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.58451728309129.1	x^7 - x^6 - 84x^5 + 217x^4 + 1348x^3 - 3988x^2 - 1433x + 1163	\( 197^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.88245939632761.1	x^7 - x^6 - 90x^5 - 69x^4 + 1306x^3 - 124x^2 - 5249x + 4663	\( 211^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.186374892382561.1	x^7 - x^6 - 102x^5 + 195x^4 + 1850x^3 - 978x^2 - 8933x - 5183	\( 239^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.492309163417681.1	x^7 - x^6 - 120x^5 + 711x^4 - 784x^3 - 1956x^2 + 2863x + 343	\( 281^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.1464803622199009.1	x^7 - x^6 - 144x^5 - 399x^4 + 2416x^3 + 10808x^2 + 10831x + 1237	\( 337^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.2963706958323721.1	x^7 - x^6 - 162x^5 + 201x^4 + 7822x^3 - 12322x^2 - 107717x + 193369	\( 379^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.5567914722008521.1	x^7 - x^6 - 180x^5 + 103x^4 + 6180x^3 - 11596x^2 - 25209x + 49213	\( 421^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.8193662024284801.1	x^7 - x^6 - 192x^5 - 275x^4 + 3952x^3 - 4136x^2 - 81x + 863	\( 449^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.9851127637605409.1	x^7 - x^6 - 198x^5 + 907x^4 + 4302x^3 - 20582x^2 - 18973x + 56911	\( 463^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.14011639427134441.1	x^7 - x^6 - 210x^5 - 1423x^4 - 1410x^3 + 8538x^2 + 9203x - 19427	\( 491^{6} \)	$C_7$ (as 7T1)	$[2, 2, 2]$
7.7.26786992617986329.1	x^7 - x^6 - 234x^5 - 335x^4 + 13254x^3 + 42874x^2 - 55309x - 71879	\( 547^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.55171016309022769.1	x^7 - x^6 - 264x^5 + 151x^4 + 13288x^3 - 18556x^2 - 69425x - 34621	\( 617^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.63121332085847281.1	x^7 - x^6 - 270x^5 - 116x^4 + 19848x^3 + 31904x^2 - 375552x - 720896	\( 631^{6} \)	$C_7$ (as 7T1)	Trivial (GRH)
7.7.81905390937410041.1	x^7 - x^6 - 282x^5 - 1345x^4 + 5370x^3 + 30042x^2 - 14893x - 115169	\( 659^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.92915974333361089.1	x^7 - x^6 - 288x^5 - 316x^4 + 23504x^3 + 53056x^2 - 541952x - 1722368	\( 673^{6} \)	$C_7$ (as 7T1)	Trivial (GRH)
7.7.118661028367354201.1	x^7 - x^6 - 300x^5 - 1631x^4 + 5140x^3 + 23794x^2 - 59049x + 18773	\( 701^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.168241403464173649.1	x^7 - x^6 - 318x^5 + 1031x^4 + 26070x^3 - 125148x^2 - 420841x + 2302639	\( 743^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.188180785490436649.1	x^7 - x^6 - 324x^5 + 1483x^4 + 20876x^3 - 129744x^2 + 36999x + 54027	\( 757^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.319913861015774089.1	x^7 - x^6 - 354x^5 - 979x^4 + 30030x^3 + 111552x^2 - 715705x - 2921075	\( 827^{6} \)	$C_7$ (as 7T1)	$[2, 2, 2]$
7.7.473984589097059769.1	x^7 - x^6 - 378x^5 + 973x^4 + 13106x^3 + 9624x^2 - 64665x - 91125	\( 883^{6} \)	$C_7$ (as 7T1)	Trivial (GRH)
7.7.571623746239596961.1	x^7 - x^6 - 390x^5 + 223x^4 + 18058x^3 - 30856x^2 - 116657x + 225929	\( 911^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.749130369924173329.1	x^7 - x^6 - 408x^5 - 992x^4 + 48064x^3 + 204560x^2 - 1603520x - 8290816	\( 953^{6} \)	$C_7$ (as 7T1)	$[71]$
7.7.817633815294109969.1	x^7 - x^6 - 414x^5 + 4381x^4 - 10434x^3 - 32702x^2 + 167651x - 182573	\( 967^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.1055229678769825441.1	x^7 - x^6 - 432x^5 + 247x^4 + 59784x^3 - 15272x^2 - 2647129x - 374699	\( 1009^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.1347771585762793801.1	x^7 - x^6 - 450x^5 - 4247x^4 - 6450x^3 + 22774x^2 + 25691x + 5653	\( 1051^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.1704986606307341449.1	x^7 - x^6 - 468x^5 - 2543x^4 + 23004x^3 + 169598x^2 + 130839x - 450131	\( 1093^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.2474447753486836009.1	x^7 - x^6 - 498x^5 + 1780x^4 + 72184x^3 - 361600x^2 - 2988416x + 16876544	\( 1163^{6} \)	$C_7$ (as 7T1)	Trivial (GRH)
7.7.4586881327254923761.1	x^7 - x^6 - 552x^5 - 5577x^4 - 5280x^3 + 59010x^2 - 42769x - 7019	\( 1289^{6} \)	$C_7$ (as 7T1)	Trivial (GRH)
7.7.4894028501935246129.1	x^7 - x^6 - 558x^5 - 4893x^4 + 17638x^3 + 254174x^2 + 353419x - 218405	\( 1303^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.6699204317182001689.1	x^7 - x^6 - 588x^5 + 1513x^4 + 65884x^3 + 33346x^2 - 962361x - 55903	\( 1373^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.8233120419813614521.1	x^7 - 609x^5 - 2030x^4 + 70847x^3 + 133980x^2 - 1467487x - 2403694	\( 7^{12}\cdot 29^{6} \)	$C_7$ (as 7T1)	$[7]$ (GRH)
7.7.8233120419813614521.2	x^7 - 609x^5 - 2233x^4 + 36743x^3 + 62118x^2 - 576520x + 3625	\( 7^{12}\cdot 29^{6} \)	$C_7$ (as 7T1)	$[7]$
7.7.8233120419813614521.3	x^7 - 609x^5 - 2233x^4 + 48111x^3 - 40194x^2 - 87696x + 77517	\( 7^{12}\cdot 29^{6} \)	$C_7$ (as 7T1)	$[7]$
7.7.8233120419813614521.4	x^7 - 609x^5 - 609x^4 + 104951x^3 + 119770x^2 - 5123720x - 9825577	\( 7^{12}\cdot 29^{6} \)	$C_7$ (as 7T1)	$[7]$
7.7.8233120419813614521.5	x^7 - 609x^5 - 609x^4 + 36743x^3 + 162400x^2 + 179452x - 12151	\( 7^{12}\cdot 29^{6} \)	$C_7$ (as 7T1)	$[7]$
7.7.8233120419813614521.6	x^7 - 609x^5 - 6293x^4 + 2639x^3 + 125454x^2 - 133168x + 30479	\( 7^{12}\cdot 29^{6} \)	$C_7$ (as 7T1)	$[7]$
7.7.8515170979269874921.1	x^7 - x^6 - 612x^5 + 1983x^4 + 118732x^3 - 607744x^2 - 6889121x + 43521943	\( 1429^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.10131553366728232321.1	x^7 - x^6 - 630x^5 - 1321x^4 + 105050x^3 + 532744x^2 - 1423169x - 1017227	\( 1471^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.11345138370033741001.1	x^7 - x^6 - 642x^5 + 367x^4 + 114514x^3 - 287002x^2 - 6382709x + 28440251	\( 1499^{6} \)	$C_7$ (as 7T1)	Trivial
7.7.15735679056639910369.1	x^7 - x^6 - 678x^5 - 517x^4 + 79450x^3 - 44802x^2 - 1841157x + 1084293	\( 1583^{6} \)	$C_7$ (as 7T1)	Trivial (GRH)
7.7.16589354847268067929.1	x^7 - x^6 - 684x^5 + 391x^4 + 101924x^3 + 148956x^2 - 2012697x - 4567671	\( 1597^{6} \)	$C_7$ (as 7T1)	Trivial (GRH)
7.7.21459203535665809369.1	x^7 - x^6 - 714x^5 + 1837x^4 + 97138x^3 + 129892x^2 - 1667073x - 2477977	\( 1667^{6} \)	$C_7$ (as 7T1)	Trivial (GRH)
7.7.24914511498062181241.1	x^7 - x^6 - 732x^5 + 3104x^4 + 155808x^3 - 1028208x^2 - 6517504x + 42320896	\( 1709^{6} \)	$C_7$ (as 7T1)	Trivial (GRH)
7.7.26164453299826084489.1	x^7 - x^6 - 738x^5 + 9283x^4 - 11418x^3 - 331708x^2 + 1727391x - 2487539	\( 1723^{6} \)	$C_7$ (as 7T1)	Trivial (GRH)