Artin Representation Search Results

Dimension	Conductor	Group	Root number	Parity
Smallest container	Ramified primes	Unramified primes	Frobenius-Schur indicator

Results (displaying matches 1-50 of )

Galois conjugate representations are grouped into single lines.

Label	Dimension	Conductor	Defining polynomial of Artin field	$G$	Ind	$\chi(c)$
10.11e4_41e6.30t176.2c1	$10$	$ 11^{4} \cdot 41^{6}$	x^6 - x^5 - 4x^4 + 6x^3 - 6x + 5	$S_6$	$1$	$-2$
10.2e8_3e20_5e4.30t176.2c1	$10$	$ 2^{8} \cdot 3^{20} \cdot 5^{4}$	x^6 + 3x^4 - 4x^3 + 9x^2 - 6x + 1	$S_6$	$1$	$-2$
10.2e24_3e16.30t88.1c1	$10$	$ 2^{24} \cdot 3^{16}$	x^6 - 3x^5 + 3x^4 - 6x^2 + 6x - 2	$A_6$	$1$	$-2$
10.2e8_3e12_7e8.30t176.2c1	$10$	$ 2^{8} \cdot 3^{12} \cdot 7^{8}$	x^6 + 5x^4 - 2x^3 + 9x^2 - 8x + 16	$S_6$	$1$	$2$
10.2e24_3e8_5e6.30t176.3c1	$10$	$ 2^{24} \cdot 3^{8} \cdot 5^{6}$	x^6 - 2x^5 - x^4 + 6x^3 - 2x^2 - 4x - 1	$S_6$	$1$	$-2$
10.2e24_3e8_5e6.30t176.4c1	$10$	$ 2^{24} \cdot 3^{8} \cdot 5^{6}$	x^6 - 2x^5 - x^4 + 6x^3 - 2x^2 - 4x - 1	$S_6$	$1$	$-2$
10.3e4_167e6.30t176.1c1	$10$	$ 3^{4} \cdot 167^{6}$	x^6 + 2x^2 - x + 1	$S_6$	$1$	$-2$
10.17e6_101e4.30t176.1c1	$10$	$ 17^{6} \cdot 101^{4}$	x^6 - 2x^5 + x^4 + x^3 - 2x^2 + x + 1	$S_6$	$1$	$-2$
10.3e14_29e6.30t88.1c1	$10$	$ 3^{14} \cdot 29^{6}$	x^6 - 3x^3 - 3x + 4	$A_6$	$1$	$-2$
10.2e26_3e16.30t176.4c1	$10$	$ 2^{26} \cdot 3^{16}$	x^6 - 2x^5 + x^4 + x^2 - 2x - 1	$S_6$	$1$	$-2$
10.2e26_3e16.30t176.2c1	$10$	$ 2^{26} \cdot 3^{16}$	x^6 - 6x^4 - 4x^3 + 6x^2 - 6	$S_6$	$1$	$-2$
10.2e20_3e20.30t176.2c1	$10$	$ 2^{20} \cdot 3^{20}$	x^6 + 3x^4 - 4x^3 - 6x - 2	$S_6$	$1$	$-2$
10.3e14_31e6.30t88.2c1	$10$	$ 3^{14} \cdot 31^{6}$	x^6 - x^3 - 3x^2 - 1	$A_6$	$1$	$-2$
10.2e6_47e4_61e4.30t176.1c1	$10$	$ 2^{6} \cdot 47^{4} \cdot 61^{4}$	x^6 - x^5 - x^3 + x + 1	$S_6$	$1$	$-2$
10.2e12_101e6.30t176.1c1	$10$	$ 2^{12} \cdot 101^{6}$	x^6 - x^5 + x^4 - x^3 + 3x^2 + 1	$S_6$	$1$	$-2$
10.3e14_5e6_17e4.30t176.1c1	$10$	$ 3^{14} \cdot 5^{6} \cdot 17^{4}$	x^6 - 4x^3 - 3x^2 - 3x - 1	$S_6$	$1$	$-2$
10.3e14_193e4.30t176.1c1	$10$	$ 3^{14} \cdot 193^{4}$	x^6 - 2x^3 - 3x^2 - 3x - 1	$S_6$	$1$	$-2$
10.2e24_3e4_7e8.30t176.2c1	$10$	$ 2^{24} \cdot 3^{4} \cdot 7^{8}$	x^6 - 4x^4 - 2x^3 + x^2 - 2x - 5	$S_6$	$1$	$-2$
10.2e6_3e12_5e12.30t176.1c1	$10$	$ 2^{6} \cdot 3^{12} \cdot 5^{12}$	x^6 - 3x^5 + 5x^3 - 5	$S_6$	$1$	$-2$
10.2e6_3e12_5e12.30t176.2c1	$10$	$ 2^{6} \cdot 3^{12} \cdot 5^{12}$	x^6 - 3x^5 + 5x^3 - 5	$S_6$	$1$	$-2$
10.11e6_41e6.30t176.2c1	$10$	$ 11^{6} \cdot 41^{6}$	x^6 - x^5 - 4x^4 + 6x^3 - 6x + 5	$S_6$	$1$	$2$
10.3e14_5e6_7e6.30t88.2c1	$10$	$ 3^{14} \cdot 5^{6} \cdot 7^{6}$	x^6 + 3x^4 - 12x^2 - 15x + 16	$A_6$	$1$	$-2$
10.2e6_3461e4.30t176.1c1	$10$	$ 2^{6} \cdot 3461^{4}$	x^6 - x^5 - 2x^4 + 3x^3 - x + 1	$S_6$	$1$	$-2$
10.3e16_11e8.30t176.1c1	$10$	$ 3^{16} \cdot 11^{8}$	x^6 + 3x^4 - 2x^3 + 6x^2 + 9x + 5	$S_6$	$1$	$2$
10.3e16_11e8.30t176.2c1	$10$	$ 3^{16} \cdot 11^{8}$	x^6 + 3x^4 - 2x^3 + 6x^2 + 9x + 5	$S_6$	$1$	$-2$
10.2e16_5e16.30t176.2c1	$10$	$ 2^{16} \cdot 5^{16}$	x^6 - 3x^5 + 5x^4 - 5x^3 + 10x^2 - 4x - 8	$S_6$	$1$	$-2$
10.3e16_5e12.30t176.1c1	$10$	$ 3^{16} \cdot 5^{12}$	x^6 - 3x^5 + 15x^2 - 3x - 1	$S_6$	$1$	$-2$
10.3e16_5e12.30t176.2c1	$10$	$ 3^{16} \cdot 5^{12}$	x^6 - 3x^5 + 15x^2 - 3x - 1	$S_6$	$1$	$-2$
10.2e28_3e16.30t176.1c1	$10$	$ 2^{28} \cdot 3^{16}$	x^6 - 6x^4 - 4x^3 + 6x^2 - 6	$S_6$	$1$	$-2$
10.2e12_3e12_7e8.30t176.2c1	$10$	$ 2^{12} \cdot 3^{12} \cdot 7^{8}$	x^6 + 5x^4 - 2x^3 + 9x^2 - 8x + 16	$S_6$	$1$	$-2$
10.2e8_3e20_5e6.30t176.2c1	$10$	$ 2^{8} \cdot 3^{20} \cdot 5^{6}$	x^6 + 3x^4 - 4x^3 + 9x^2 - 6x + 1	$S_6$	$1$	$-2$
10.2e9_3e14_7e8.70.1c1 10.2e9_3e14_7e8.70.1c2	$10$	$ 2^{9} \cdot 3^{14} \cdot 7^{8}$	x^7 - 3x^6 + 3x^5 + 3x^4 - 9x^3 + 3x^2 + x - 3	$A_7$	$0$	$-2$
10.2e22_3e20.30t176.2c1	$10$	$ 2^{22} \cdot 3^{20}$	x^6 + 3x^4 - 4x^3 - 6x - 2	$S_6$	$1$	$-2$
10.3e6_167e6.30t176.1c1	$10$	$ 3^{6} \cdot 167^{6}$	x^6 + 2x^2 - x + 1	$S_6$	$1$	$2$
10.2e26_5e12.30t176.1c1	$10$	$ 2^{26} \cdot 5^{12}$	x^6 - 2x^5 + 5x^4 - 10x^2 + 8x - 6	$S_6$	$1$	$-2$
10.2e6_3e12_149e4.30t176.1c1	$10$	$ 2^{6} \cdot 3^{12} \cdot 149^{4}$	x^6 - x^5 + 2x^4 + x^3 - 2x^2 + x + 1	$S_6$	$1$	$-2$
10.3e20_13e6.30t88.1c1	$10$	$ 3^{20} \cdot 13^{6}$	x^6 - 3x^5 + 3x^4 - 3x^2 + 3x + 2	$A_6$	$1$	$-2$
10.3e20_7e8.30t88.2c1	$10$	$ 3^{20} \cdot 7^{8}$	x^6 - 3x^5 + 3x^4 + 9x^3 - 18x^2 - 9x + 18	$A_6$	$1$	$-2$
10.2e18_67e6.30t88.1c1	$10$	$ 2^{18} \cdot 67^{6}$	x^6 - 2x^4 + x^2 - 2x - 1	$A_6$	$1$	$-2$
10.3e12_461e4.30t176.1c1	$10$	$ 3^{12} \cdot 461^{4}$	x^6 - 3x^5 + 3x^4 + 2x^3 - 6x^2 + 3x + 1	$S_6$	$1$	$-2$
10.3e14_277e4.30t176.1c1	$10$	$ 3^{14} \cdot 277^{4}$	x^6 - 3x^4 + 3x^2 - 3x + 1	$S_6$	$1$	$-2$
10.5e4_191e6.30t176.1c1	$10$	$ 5^{4} \cdot 191^{6}$	x^6 - x^4 - 3x^3 + x + 3	$S_6$	$1$	$-2$
10.2e18_587e4.30t176.1c1	$10$	$ 2^{18} \cdot 587^{4}$	x^6 - 2x^5 + 2x^4 - x^2 + 2x - 1	$S_6$	$1$	$-2$
10.3e14_17e8.30t176.3c1	$10$	$ 3^{14} \cdot 17^{8}$	x^6 - x^5 - 2x^4 + x^3 + 14x^2 - 17x + 6	$S_6$	$1$	$2$
10.3e14_17e8.30t176.4c1	$10$	$ 3^{14} \cdot 17^{8}$	x^6 - x^5 - 2x^4 + x^3 + 14x^2 - 17x + 6	$S_6$	$1$	$-2$
10.2e6_3e4_17e6_23e4.30t176.1c1	$10$	$ 2^{6} \cdot 3^{4} \cdot 17^{6} \cdot 23^{4}$	x^6 - x^5 - 2x^4 + 3x^3 - 2x^2 + 3x - 3	$S_6$	$1$	$-2$
10.2e24_223e4.30t176.1c1	$10$	$ 2^{24} \cdot 223^{4}$	x^6 - 2x^5 + 4x^3 - 4x^2 + 2	$S_6$	$1$	$-2$
10.14731e4.30t176.1c1	$10$	$ 14731^{4}$	x^6 - x^5 + x^3 - x^2 + 1	$S_6$	$1$	$-2$
10.2e18_3e12_5e8.30t176.3c1	$10$	$ 2^{18} \cdot 3^{12} \cdot 5^{8}$	x^6 + 2x^4 - 2x^3 - 3x^2 - 6x - 3	$S_6$	$1$	$-2$
10.2e18_3e12_5e8.30t176.4c1	$10$	$ 2^{18} \cdot 3^{12} \cdot 5^{8}$	x^6 + 2x^4 - 2x^3 - 3x^2 - 6x - 3	$S_6$	$1$	$-2$