LMFDB - Complex character search results

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Degree	Type	Faithful	Conductor

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Results (21 matches)

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Label	Degree	Type	Faithful	Conductor	Field of Traces	$\Q$-character	Group	Image	Image Order	Kernel	Kernel Order	Center	Center Order	Center Index	Schur Index
48.27.1a	$1$	R		$1$	$\Q$	48.27.1a	$C_3\times Q_{16}$	$C_1$	$1$	1.a1.a1	$48$	1.a1.a1	$48$	$1$	$1$
48.27.1b	$1$	R		$1$	$\Q$	48.27.1b	$C_3\times Q_{16}$	$C_2$	$2$	2.b1.a1	$24$	1.a1.a1	$48$	$1$	$1$
48.27.1c	$1$	R		$1$	$\Q$	48.27.1c	$C_3\times Q_{16}$	$C_2$	$2$	2.a1.b1	$24$	1.a1.a1	$48$	$1$	$1$
48.27.1d	$1$	R		$1$	$\Q$	48.27.1d	$C_3\times Q_{16}$	$C_2$	$2$	2.a1.a1	$24$	1.a1.a1	$48$	$1$	$1$
48.27.1e1	$1$	C		$3$	$\Q(\sqrt{-3}) $	48.27.1e	$C_3\times Q_{16}$	$C_3$	$3$	3.a1.a1	$16$	1.a1.a1	$48$	$1$	$1$
48.27.1e2	$1$	C		$3$	$\Q(\sqrt{-3}) $	48.27.1e	$C_3\times Q_{16}$	$C_3$	$3$	3.a1.a1	$16$	1.a1.a1	$48$	$1$	$1$
48.27.1f1	$1$	C		$3$	$\Q(\sqrt{-3}) $	48.27.1f	$C_3\times Q_{16}$	$C_6$	$6$	6.b1.a1	$8$	1.a1.a1	$48$	$1$	$1$
48.27.1f2	$1$	C		$3$	$\Q(\sqrt{-3}) $	48.27.1f	$C_3\times Q_{16}$	$C_6$	$6$	6.b1.a1	$8$	1.a1.a1	$48$	$1$	$1$
48.27.1g1	$1$	C		$3$	$\Q(\sqrt{-3}) $	48.27.1g	$C_3\times Q_{16}$	$C_6$	$6$	6.a1.b1	$8$	1.a1.a1	$48$	$1$	$1$
48.27.1g2	$1$	C		$3$	$\Q(\sqrt{-3}) $	48.27.1g	$C_3\times Q_{16}$	$C_6$	$6$	6.a1.b1	$8$	1.a1.a1	$48$	$1$	$1$
48.27.1h1	$1$	C		$3$	$\Q(\sqrt{-3}) $	48.27.1h	$C_3\times Q_{16}$	$C_6$	$6$	6.a1.a1	$8$	1.a1.a1	$48$	$1$	$1$
48.27.1h2	$1$	C		$3$	$\Q(\sqrt{-3}) $	48.27.1h	$C_3\times Q_{16}$	$C_6$	$6$	6.a1.a1	$8$	1.a1.a1	$48$	$1$	$1$
48.27.2a	$2$	R		$1$	$\Q$	48.27.2a	$C_3\times Q_{16}$	$D_4$	$8$	8.a1.a1	$6$	4.a1.a1	$12$	$4$	$1$
48.27.2b1	$2$	C		$3$	$\Q(\sqrt{-3}) $	48.27.2b	$C_3\times Q_{16}$	$C_3\times D_4$	$24$	24.a1.a1	$2$	4.a1.a1	$12$	$4$	$1$
48.27.2b2	$2$	C		$3$	$\Q(\sqrt{-3}) $	48.27.2b	$C_3\times Q_{16}$	$C_3\times D_4$	$24$	24.a1.a1	$2$	4.a1.a1	$12$	$4$	$1$
48.27.2c1	$2$	S		$8$	$\Q(\sqrt{2}) $	48.27.2c	$C_3\times Q_{16}$	$Q_{16}$	$16$	16.a1.a1	$3$	8.a1.a1	$6$	$8$	$2$
48.27.2c2	$2$	S		$8$	$\Q(\sqrt{2}) $	48.27.2c	$C_3\times Q_{16}$	$Q_{16}$	$16$	16.a1.a1	$3$	8.a1.a1	$6$	$8$	$2$
48.27.2d1	$2$	C	✓	$24$	$\Q(\sqrt{2}, \sqrt{-3})$	48.27.2d	$C_3\times Q_{16}$	$C_3\times Q_{16}$	$48$	48.a1.a1	$1$	8.a1.a1	$6$	$8$	$1$
48.27.2d2	$2$	C	✓	$24$	$\Q(\sqrt{2}, \sqrt{-3})$	48.27.2d	$C_3\times Q_{16}$	$C_3\times Q_{16}$	$48$	48.a1.a1	$1$	8.a1.a1	$6$	$8$	$1$
48.27.2d3	$2$	C	✓	$24$	$\Q(\sqrt{2}, \sqrt{-3})$	48.27.2d	$C_3\times Q_{16}$	$C_3\times Q_{16}$	$48$	48.a1.a1	$1$	8.a1.a1	$6$	$8$	$1$
48.27.2d4	$2$	C	✓	$24$	$\Q(\sqrt{2}, \sqrt{-3})$	48.27.2d	$C_3\times Q_{16}$	$C_3\times Q_{16}$	$48$	48.a1.a1	$1$	8.a1.a1	$6$	$8$	$1$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
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Results (21 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	Degree	Type	Faithful	Conductor	Field of Traces	$\Q$-character	Group	Image	Image Order	Kernel	Kernel Order	Center	Center Order	Center Index	Schur Index
48.27.1a	$1$	R		$1$	\(\Q\)	48.27.1a	$C_3\times Q_{16}$	$C_1$	$1$	1.a1.a1	$48$	1.a1.a1	$48$	$1$	$1$
48.27.1b	$1$	R		$1$	\(\Q\)	48.27.1b	$C_3\times Q_{16}$	$C_2$	$2$	2.b1.a1	$24$	1.a1.a1	$48$	$1$	$1$
48.27.1c	$1$	R		$1$	\(\Q\)	48.27.1c	$C_3\times Q_{16}$	$C_2$	$2$	2.a1.b1	$24$	1.a1.a1	$48$	$1$	$1$
48.27.1d	$1$	R		$1$	\(\Q\)	48.27.1d	$C_3\times Q_{16}$	$C_2$	$2$	2.a1.a1	$24$	1.a1.a1	$48$	$1$	$1$
48.27.1e1	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	48.27.1e	$C_3\times Q_{16}$	$C_3$	$3$	3.a1.a1	$16$	1.a1.a1	$48$	$1$	$1$
48.27.1e2	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	48.27.1e	$C_3\times Q_{16}$	$C_3$	$3$	3.a1.a1	$16$	1.a1.a1	$48$	$1$	$1$
48.27.1f1	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	48.27.1f	$C_3\times Q_{16}$	$C_6$	$6$	6.b1.a1	$8$	1.a1.a1	$48$	$1$	$1$
48.27.1f2	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	48.27.1f	$C_3\times Q_{16}$	$C_6$	$6$	6.b1.a1	$8$	1.a1.a1	$48$	$1$	$1$
48.27.1g1	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	48.27.1g	$C_3\times Q_{16}$	$C_6$	$6$	6.a1.b1	$8$	1.a1.a1	$48$	$1$	$1$
48.27.1g2	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	48.27.1g	$C_3\times Q_{16}$	$C_6$	$6$	6.a1.b1	$8$	1.a1.a1	$48$	$1$	$1$
48.27.1h1	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	48.27.1h	$C_3\times Q_{16}$	$C_6$	$6$	6.a1.a1	$8$	1.a1.a1	$48$	$1$	$1$
48.27.1h2	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	48.27.1h	$C_3\times Q_{16}$	$C_6$	$6$	6.a1.a1	$8$	1.a1.a1	$48$	$1$	$1$
48.27.2a	$2$	R		$1$	\(\Q\)	48.27.2a	$C_3\times Q_{16}$	$D_4$	$8$	8.a1.a1	$6$	4.a1.a1	$12$	$4$	$1$
48.27.2b1	$2$	C		$3$	\(\Q(\sqrt{-3}) \)	48.27.2b	$C_3\times Q_{16}$	$C_3\times D_4$	$24$	24.a1.a1	$2$	4.a1.a1	$12$	$4$	$1$
48.27.2b2	$2$	C		$3$	\(\Q(\sqrt{-3}) \)	48.27.2b	$C_3\times Q_{16}$	$C_3\times D_4$	$24$	24.a1.a1	$2$	4.a1.a1	$12$	$4$	$1$
48.27.2c1	$2$	S		$8$	\(\Q(\sqrt{2}) \)	48.27.2c	$C_3\times Q_{16}$	$Q_{16}$	$16$	16.a1.a1	$3$	8.a1.a1	$6$	$8$	$2$
48.27.2c2	$2$	S		$8$	\(\Q(\sqrt{2}) \)	48.27.2c	$C_3\times Q_{16}$	$Q_{16}$	$16$	16.a1.a1	$3$	8.a1.a1	$6$	$8$	$2$
48.27.2d1	$2$	C	✓	$24$	\(\Q(\sqrt{2}, \sqrt{-3})\)	48.27.2d	$C_3\times Q_{16}$	$C_3\times Q_{16}$	$48$	48.a1.a1	$1$	8.a1.a1	$6$	$8$	$1$
48.27.2d2	$2$	C	✓	$24$	\(\Q(\sqrt{2}, \sqrt{-3})\)	48.27.2d	$C_3\times Q_{16}$	$C_3\times Q_{16}$	$48$	48.a1.a1	$1$	8.a1.a1	$6$	$8$	$1$
48.27.2d3	$2$	C	✓	$24$	\(\Q(\sqrt{2}, \sqrt{-3})\)	48.27.2d	$C_3\times Q_{16}$	$C_3\times Q_{16}$	$48$	48.a1.a1	$1$	8.a1.a1	$6$	$8$	$1$
48.27.2d4	$2$	C	✓	$24$	\(\Q(\sqrt{2}, \sqrt{-3})\)	48.27.2d	$C_3\times Q_{16}$	$C_3\times Q_{16}$	$48$	48.a1.a1	$1$	8.a1.a1	$6$	$8$	$1$