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 115)

Galois conjugate representations are grouped into single lines.

Label	Dimension	Conductor	Defining polynomial of Artin field	$G$	Ind	$\chi(c)$
5.2e6_67e2.6t15.1c1	$5$	$ 2^{6} \cdot 67^{2}$	x^6 - 2x^4 + x^2 - 2x - 1	$A_6$	$1$	$1$
5.3e6_29e2.6t15.1c1	$5$	$ 3^{6} \cdot 29^{2}$	x^6 - 3x^3 - 3x + 4	$A_6$	$1$	$1$
5.3e6_31e2.6t15.2c1	$5$	$ 3^{6} \cdot 31^{2}$	x^6 - x^3 - 3x^2 - 1	$A_6$	$1$	$1$
5.7e2_149e2.6t15.2c1	$5$	$ 7^{2} \cdot 149^{2}$	x^6 - x^5 + 2x^4 - 3x^2 + 2x - 4	$A_6$	$1$	$1$
5.3e8_13e2.6t15.1c1	$5$	$ 3^{8} \cdot 13^{2}$	x^6 - 3x^5 + 3x^4 - 3x^2 + 3x + 2	$A_6$	$1$	$1$
5.2e6_7e2_23e2.6t15.2c1	$5$	$ 2^{6} \cdot 7^{2} \cdot 23^{2}$	x^6 - 3x^5 + 5x^4 - 8x^2 + 4x + 4	$A_6$	$1$	$1$
5.2e8_3e8.6t15.1c1	$5$	$ 2^{8} \cdot 3^{8}$	x^6 - 3x^5 + 3x^4 - 6x^2 + 6x - 2	$A_6$	$1$	$1$
5.2e4_3e6_13e2.6t15.2c1	$5$	$ 2^{4} \cdot 3^{6} \cdot 13^{2}$	x^6 - 3x^5 + 3x^4 - 2	$A_6$	$1$	$1$
5.2e6_7e2_31e2.6t15.1c1	$5$	$ 2^{6} \cdot 7^{2} \cdot 31^{2}$	x^6 - 2x^5 + x^4 - 2x^3 - x^2 + 6x - 1	$A_6$	$1$	$1$
5.2e10_3e8.6t15.1c1	$5$	$ 2^{10} \cdot 3^{8}$	x^6 - 3x^5 + 3x^4 - 6x^2 + 6x - 2	$A_6$	$1$	$1$
5.2e6_3e6_13e2.6t15.2c1	$5$	$ 2^{6} \cdot 3^{6} \cdot 13^{2}$	x^6 - 3x^5 + 3x^4 - 2	$A_6$	$1$	$1$
5.3e8_7e4.6t15.2c1	$5$	$ 3^{8} \cdot 7^{4}$	x^6 - 3x^5 + 3x^4 + 9x^3 - 18x^2 - 9x + 18	$A_6$	$1$	$1$
5.13e2_19e4.6t15.2c1	$5$	$ 13^{2} \cdot 19^{4}$	x^6 - 4x^4 - 15x^3 - 15x^2 - 8x + 4	$A_6$	$1$	$1$
5.3e6_5e4_7e2.6t15.2c1	$5$	$ 3^{6} \cdot 5^{4} \cdot 7^{2}$	x^6 + 3x^4 - 12x^2 - 15x + 16	$A_6$	$1$	$1$
5.2e12_3e8.6t15.2c1	$5$	$ 2^{12} \cdot 3^{8}$	x^6 + 6x^4 - 4x^3 - 3x^2 - 12x - 12	$A_6$	$1$	$1$
5.2e12_3e8.6t15.3c1	$5$	$ 2^{12} \cdot 3^{8}$	x^6 - 8x^3 + 9x^2 - 6	$A_6$	$1$	$1$
5.2e4_7e4_31e2.6t15.1c1	$5$	$ 2^{4} \cdot 7^{4} \cdot 31^{2}$	x^6 - 2x^5 + x^4 - 2x^3 - x^2 + 6x - 1	$A_6$	$1$	$1$
5.3e6_5e2_7e4.6t15.2c1	$5$	$ 3^{6} \cdot 5^{2} \cdot 7^{4}$	x^6 + 3x^4 - 12x^2 - 15x + 16	$A_6$	$1$	$1$
5.7e4_149e2.6t15.2c1	$5$	$ 7^{4} \cdot 149^{2}$	x^6 - x^5 + 2x^4 - 3x^2 + 2x - 4	$A_6$	$1$	$1$
5.2e8_23e4.6t15.1c1	$5$	$ 2^{8} \cdot 23^{4}$	x^6 - x^5 + x^4 + 4x^3 - 6x^2 + 2x + 2	$A_6$	$1$	$1$
5.2e6_7e4_23e2.6t15.2c1	$5$	$ 2^{6} \cdot 7^{4} \cdot 23^{2}$	x^6 - 3x^5 + 5x^4 - 8x^2 + 4x + 4	$A_6$	$1$	$1$
5.3e6_19e4.6t15.2c1	$5$	$ 3^{6} \cdot 19^{4}$	x^6 - 3x^5 - 3x^4 + 8x^3 + 9x^2 - 9x + 6	$A_6$	$1$	$1$
5.2e14_3e8.6t15.1c1	$5$	$ 2^{14} \cdot 3^{8}$	x^6 - 12x^3 + 21x^2 + 12x - 34	$A_6$	$1$	$1$
5.5e8_17e2.6t15.2c1	$5$	$ 5^{8} \cdot 17^{2}$	x^6 - 2x^5 + 5x^2 - 11x - 13	$A_6$	$1$	$1$
5.5e8_17e2.6t15.1c1	$5$	$ 5^{8} \cdot 17^{2}$	x^6 - 2x^5 + 5x^2 - 11x - 13	$A_6$	$1$	$1$
5.3e10_7e4.6t15.2c1	$5$	$ 3^{10} \cdot 7^{4}$	x^6 - 3x^5 + 3x^4 + 9x^3 - 18x^2 - 9x + 18	$A_6$	$1$	$1$
5.3e8_7e2_23e2.6t15.1c1	$5$	$ 3^{8} \cdot 7^{2} \cdot 23^{2}$	x^6 - 3x^5 - 9x^4 + 14x^3 + 27x^2 - 3x - 10	$A_6$	$1$	$5$
5.7e4_283e2.6t15.1c1	$5$	$ 7^{4} \cdot 283^{2}$	x^6 - x^5 - 12x^4 + 7x^3 + 21x^2 - 7x - 7	$A_6$	$1$	$5$
5.2e12_3e10.6t15.2c1	$5$	$ 2^{12} \cdot 3^{10}$	x^6 + 6x^4 - 4x^3 - 3x^2 - 12x - 12	$A_6$	$1$	$1$
5.2e12_3e10.6t15.3c1	$5$	$ 2^{12} \cdot 3^{10}$	x^6 - 8x^3 + 9x^2 - 6	$A_6$	$1$	$1$
5.3e6_5e8.6t15.1c1	$5$	$ 3^{6} \cdot 5^{8}$	x^6 - 5x^3 + 45x^2 - 99x - 15	$A_6$	$1$	$1$
5.2e10_23e4.6t15.1c1	$5$	$ 2^{10} \cdot 23^{4}$	x^6 - x^5 + x^4 + 4x^3 - 6x^2 + 2x + 2	$A_6$	$1$	$1$
5.3e6_29e4.6t15.1c1	$5$	$ 3^{6} \cdot 29^{4}$	x^6 - 3x^3 - 3x + 4	$A_6$	$1$	$1$
5.3e6_31e4.6t15.2c1	$5$	$ 3^{6} \cdot 31^{4}$	x^6 - x^3 - 3x^2 - 1	$A_6$	$1$	$1$
5.2e14_3e10.6t15.1c1	$5$	$ 2^{14} \cdot 3^{10}$	x^6 - 12x^3 + 21x^2 + 12x - 34	$A_6$	$1$	$1$
5.2e6_67e4.6t15.1c1	$5$	$ 2^{6} \cdot 67^{4}$	x^6 - 2x^4 + x^2 - 2x - 1	$A_6$	$1$	$1$
5.3e10_13e4.6t15.1c1	$5$	$ 3^{10} \cdot 13^{4}$	x^6 - 3x^5 + 3x^4 - 3x^2 + 3x + 2	$A_6$	$1$	$1$
5.3e8_5e8.6t15.1c1	$5$	$ 3^{8} \cdot 5^{8}$	x^6 - 3x^5 + 15x^4 - 25x^3 - 45x + 60	$A_6$	$1$	$1$
5.13e4_19e4.6t15.2c1	$5$	$ 13^{4} \cdot 19^{4}$	x^6 - 4x^4 - 15x^3 - 15x^2 - 8x + 4	$A_6$	$1$	$1$
5.2e14_5e8.6t15.2c1	$5$	$ 2^{14} \cdot 5^{8}$	x^6 - 2x^5 + 15x^4 + 50x^2 - 4x - 82	$A_6$	$1$	$1$
5.2e14_5e8.6t15.1c1	$5$	$ 2^{14} \cdot 5^{8}$	x^6 - 2x^5 + 15x^4 + 50x^2 - 4x - 82	$A_6$	$1$	$1$
5.3e10_19e4.6t15.2c1	$5$	$ 3^{10} \cdot 19^{4}$	x^6 - 3x^5 - 3x^4 + 8x^3 + 9x^2 - 9x + 6	$A_6$	$1$	$1$
5.3e10_5e8.6t15.2c1	$5$	$ 3^{10} \cdot 5^{8}$	x^6 - 3x^5 + 15x^4 - 25x^3 - 45x + 60	$A_6$	$1$	$1$
5.3e10_5e8.6t15.1c1	$5$	$ 3^{10} \cdot 5^{8}$	x^6 - 5x^3 + 45x^2 - 99x - 15	$A_6$	$1$	$1$
5.3e8_7e4_23e4.6t15.1c1	$5$	$ 3^{8} \cdot 7^{4} \cdot 23^{4}$	x^6 - 3x^5 - 9x^4 + 14x^3 + 27x^2 - 3x - 10	$A_6$	$1$	$5$
5.7e4_283e4.6t15.1c1	$5$	$ 7^{4} \cdot 283^{4}$	x^6 - x^5 - 12x^4 + 7x^3 + 21x^2 - 7x - 7	$A_6$	$1$	$5$
8.2e18_3e16.36t555.1c1 8.2e18_3e16.36t555.1c2	$8$	$ 2^{18} \cdot 3^{16}$	x^6 - 3x^5 + 3x^4 - 6x^2 + 6x - 2	$A_6$	$1$	$0$
8.2e10_3e12_13e4.36t555.2c1 8.2e10_3e12_13e4.36t555.2c2	$8$	$ 2^{10} \cdot 3^{12} \cdot 13^{4}$	x^6 - 3x^5 + 3x^4 - 2	$A_6$	$1$	$0$
8.5e12_17e4.36t555.1c1 8.5e12_17e4.36t555.1c2	$8$	$ 5^{12} \cdot 17^{4}$	x^6 - 2x^5 + 5x^2 - 11x - 13	$A_6$	$1$	$0$
8.2e18_23e6.36t555.1c1 8.2e18_23e6.36t555.1c2	$8$	$ 2^{18} \cdot 23^{6}$	x^6 - x^5 + x^4 + 4x^3 - 6x^2 + 2x + 2	$A_6$	$1$	$0$