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 all 4 matches)

Label	Polynomial	Discriminant	Galois group	Class group
10.0.2872930298891221299684295654296875.1	x^10 - 6765x^7 + 696795x^6 + 83279856x^5 + 3706058675x^4 + 94284129720x^3 + 1257274742625x^2 + 10961015191335x + 85798288501893	\( -\,5^{16}\cdot 11^{9}\cdot 41^{8} \)	$C_{10}$ (as 10T1)	$[5, 5, 6779905]$ (GRH)
10.0.63465642057324252347571258544921875.1	x^10 + 4510x^8 - 266090x^7 + 21057190x^6 - 599153951x^5 + 14466896125x^4 - 87476668070x^3 + 397271646145x^2 - 630321392910x + 772639242001	\( -\,3^{5}\cdot 5^{16}\cdot 11^{8}\cdot 41^{8} \)	$C_{10}$ (as 10T1)	$[4, 4, 20, 739420]$ (GRH)
10.0.317328210286621261737856292724609375.1	x^10 + 4510x^8 - 133045x^7 + 2751100x^6 - 480905359x^5 + 706818475x^4 - 163060479670x^3 + 12256011666415x^2 + 140389724566575x + 9142215828856099	\( -\,3^{5}\cdot 5^{17}\cdot 11^{8}\cdot 41^{8} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 110, 413710]$ (GRH)
10.2.63613148112891287123047110351562500000000.1	x^10 - 5x^9 - 9690x^8 + 38790x^7 + 37577805x^6 - 112686681x^5 - 72901398000x^4 + 149531844600x^3 + 70745098715400x^2 - 67385222095700x - 27481198710005660	\( 2^{8}\cdot 3^{9}\cdot 5^{18}\cdot 13^{9}\cdot 199^{5} \)	$F_{5}\times C_2$ (as 10T5)	$[2, 2, 4, 4, 2283960]$ (GRH)