LMFDB - Complex character search results

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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
6.1.2a	$2$	R	✓	$1$	$\Q$	6.1.2a	$S_3$	$S_3$	$6$	6.a1.a1	$1$	6.a1.a1	$1$	$6$	$1$
8.3.2a	$2$	R	✓	$1$	$\Q$	8.3.2a	$D_4$	$D_4$	$8$	8.a1.a1	$1$	4.a1.a1	$2$	$4$	$1$
8.4.2a	$2$	S	✓	$1$	$\Q$	8.4.2a	$Q_8$	$Q_8$	$8$	8.a1.a1	$1$	4.a1.a1	$2$	$4$	$2$
10.1.2a1	$2$	R	✓	$5$	$\Q(\sqrt{5}) $	10.1.2a	$D_5$	$D_5$	$10$	10.a1.a1	$1$	10.a1.a1	$1$	$10$	$1$
10.1.2a2	$2$	R	✓	$5$	$\Q(\sqrt{5}) $	10.1.2a	$D_5$	$D_5$	$10$	10.a1.a1	$1$	10.a1.a1	$1$	$10$	$1$
12.1.2a	$2$	R		$1$	$\Q$	12.1.2a	$C_3:C_4$	$S_3$	$6$	6.a1.a1	$2$	6.a1.a1	$2$	$6$	$1$
12.1.2b	$2$	S	✓	$1$	$\Q$	12.1.2b	$C_3:C_4$	$C_3:C_4$	$12$	12.a1.a1	$1$	6.a1.a1	$2$	$6$	$2$
12.4.2a	$2$	R		$1$	$\Q$	12.4.2a	$D_6$	$S_3$	$6$	6.a1.a1	$2$	6.a1.a1	$2$	$6$	$1$
12.4.2b	$2$	R	✓	$1$	$\Q$	12.4.2b	$D_6$	$D_6$	$12$	12.a1.a1	$1$	6.a1.a1	$2$	$6$	$1$
14.1.2a1	$2$	R	✓	$7$	$\Q(\zeta_{7})^+$	14.1.2a	$D_7$	$D_7$	$14$	14.a1.a1	$1$	14.a1.a1	$1$	$14$	$1$
14.1.2a2	$2$	R	✓	$7$	$\Q(\zeta_{7})^+$	14.1.2a	$D_7$	$D_7$	$14$	14.a1.a1	$1$	14.a1.a1	$1$	$14$	$1$
14.1.2a3	$2$	R	✓	$7$	$\Q(\zeta_{7})^+$	14.1.2a	$D_7$	$D_7$	$14$	14.a1.a1	$1$	14.a1.a1	$1$	$14$	$1$
16.3.2a	$2$	R		$1$	$\Q$	16.3.2a	$C_2^2:C_4$	$D_4$	$8$	8.b1.b1	$2$	4.a1.a1	$4$	$4$	$1$
16.3.2b	$2$	R		$1$	$\Q$	16.3.2b	$C_2^2:C_4$	$D_4$	$8$	8.b1.a1	$2$	4.a1.a1	$4$	$4$	$1$
16.4.2a	$2$	R		$1$	$\Q$	16.4.2a	$C_4:C_4$	$D_4$	$8$	8.c1.a1	$2$	4.a1.a1	$4$	$4$	$1$
16.4.2b	$2$	S		$1$	$\Q$	16.4.2b	$C_4:C_4$	$Q_8$	$8$	8.a1.a1	$2$	4.a1.a1	$4$	$4$	$2$
16.6.2a1	$2$	C	✓	$4$	$\Q(\sqrt{-1}) $	16.6.2a	$\OD_{16}$	$\OD_{16}$	$16$	16.a1.a1	$1$	4.b1.a1	$4$	$4$	$1$
16.6.2a2	$2$	C	✓	$4$	$\Q(\sqrt{-1}) $	16.6.2a	$\OD_{16}$	$\OD_{16}$	$16$	16.a1.a1	$1$	4.b1.a1	$4$	$4$	$1$
16.7.2a	$2$	R		$1$	$\Q$	16.7.2a	$D_8$	$D_4$	$8$	8.a1.a1	$2$	4.a1.a1	$4$	$4$	$1$
16.7.2b1	$2$	R	✓	$8$	$\Q(\sqrt{2}) $	16.7.2b	$D_8$	$D_8$	$16$	16.a1.a1	$1$	8.a1.a1	$2$	$8$	$1$
16.7.2b2	$2$	R	✓	$8$	$\Q(\sqrt{2}) $	16.7.2b	$D_8$	$D_8$	$16$	16.a1.a1	$1$	8.a1.a1	$2$	$8$	$1$
16.8.2a	$2$	R		$1$	$\Q$	16.8.2a	$\SD_{16}$	$D_4$	$8$	8.a1.a1	$2$	4.a1.a1	$4$	$4$	$1$
16.8.2b1	$2$	C	✓	$8$	$\Q(\sqrt{-2}) $	16.8.2b	$\SD_{16}$	$\SD_{16}$	$16$	16.a1.a1	$1$	8.a1.a1	$2$	$8$	$1$
16.8.2b2	$2$	C	✓	$8$	$\Q(\sqrt{-2}) $	16.8.2b	$\SD_{16}$	$\SD_{16}$	$16$	16.a1.a1	$1$	8.a1.a1	$2$	$8$	$1$
16.9.2a	$2$	R		$1$	$\Q$	16.9.2a	$Q_{16}$	$D_4$	$8$	8.a1.a1	$2$	4.a1.a1	$4$	$4$	$1$
16.9.2b1	$2$	S	✓	$8$	$\Q(\sqrt{2}) $	16.9.2b	$Q_{16}$	$Q_{16}$	$16$	16.a1.a1	$1$	8.a1.a1	$2$	$8$	$2$
16.9.2b2	$2$	S	✓	$8$	$\Q(\sqrt{2}) $	16.9.2b	$Q_{16}$	$Q_{16}$	$16$	16.a1.a1	$1$	8.a1.a1	$2$	$8$	$2$
16.11.2a	$2$	R		$1$	$\Q$	16.11.2a	$C_2\times D_4$	$D_4$	$8$	8.a1.a1	$2$	4.a1.a1	$4$	$4$	$1$
16.11.2b	$2$	R		$1$	$\Q$	16.11.2b	$C_2\times D_4$	$D_4$	$8$	8.a1.b1	$2$	4.a1.a1	$4$	$4$	$1$
16.12.2a	$2$	S		$1$	$\Q$	16.12.2a	$C_2\times Q_8$	$Q_8$	$8$	8.a1.b1	$2$	4.a1.a1	$4$	$4$	$2$
16.12.2b	$2$	S		$1$	$\Q$	16.12.2b	$C_2\times Q_8$	$Q_8$	$8$	8.a1.a1	$2$	4.a1.a1	$4$	$4$	$2$
16.13.2a1	$2$	C	✓	$4$	$\Q(\sqrt{-1}) $	16.13.2a	$D_4:C_2$	$D_4:C_2$	$16$	16.a1.a1	$1$	4.b1.a1	$4$	$4$	$1$
16.13.2a2	$2$	C	✓	$4$	$\Q(\sqrt{-1}) $	16.13.2a	$D_4:C_2$	$D_4:C_2$	$16$	16.a1.a1	$1$	4.b1.a1	$4$	$4$	$1$
18.1.2a	$2$	R		$1$	$\Q$	18.1.2a	$D_9$	$S_3$	$6$	6.a1.a1	$3$	6.a1.a1	$3$	$6$	$1$
18.1.2b1	$2$	R	✓	$9$	$\Q(\zeta_{9})^+$	18.1.2b	$D_9$	$D_9$	$18$	18.a1.a1	$1$	18.a1.a1	$1$	$18$	$1$
18.1.2b2	$2$	R	✓	$9$	$\Q(\zeta_{9})^+$	18.1.2b	$D_9$	$D_9$	$18$	18.a1.a1	$1$	18.a1.a1	$1$	$18$	$1$
18.1.2b3	$2$	R	✓	$9$	$\Q(\zeta_{9})^+$	18.1.2b	$D_9$	$D_9$	$18$	18.a1.a1	$1$	18.a1.a1	$1$	$18$	$1$
18.3.2a	$2$	R		$1$	$\Q$	18.3.2a	$C_3\times S_3$	$S_3$	$6$	6.a1.a1	$3$	6.a1.a1	$3$	$6$	$1$
18.3.2b1	$2$	C	✓	$3$	$\Q(\sqrt{-3}) $	18.3.2b	$C_3\times S_3$	$C_3\times S_3$	$18$	18.a1.a1	$1$	6.a1.a1	$3$	$6$	$1$
18.3.2b2	$2$	C	✓	$3$	$\Q(\sqrt{-3}) $	18.3.2b	$C_3\times S_3$	$C_3\times S_3$	$18$	18.a1.a1	$1$	6.a1.a1	$3$	$6$	$1$
18.4.2a	$2$	R		$1$	$\Q$	18.4.2a	$C_3:S_3$	$S_3$	$6$	6.a1.d1	$3$	6.a1.d1	$3$	$6$	$1$
18.4.2b	$2$	R		$1$	$\Q$	18.4.2b	$C_3:S_3$	$S_3$	$6$	6.a1.c1	$3$	6.a1.c1	$3$	$6$	$1$
18.4.2c	$2$	R		$1$	$\Q$	18.4.2c	$C_3:S_3$	$S_3$	$6$	6.a1.b1	$3$	6.a1.b1	$3$	$6$	$1$
18.4.2d	$2$	R		$1$	$\Q$	18.4.2d	$C_3:S_3$	$S_3$	$6$	6.a1.a1	$3$	6.a1.a1	$3$	$6$	$1$
20.1.2a1	$2$	R		$5$	$\Q(\sqrt{5}) $	20.1.2a	$C_5:C_4$	$D_5$	$10$	10.a1.a1	$2$	10.a1.a1	$2$	$10$	$1$
20.1.2a2	$2$	R		$5$	$\Q(\sqrt{5}) $	20.1.2a	$C_5:C_4$	$D_5$	$10$	10.a1.a1	$2$	10.a1.a1	$2$	$10$	$1$
20.1.2b1	$2$	S	✓	$5$	$\Q(\sqrt{5}) $	20.1.2b	$C_5:C_4$	$C_5:C_4$	$20$	20.a1.a1	$1$	10.a1.a1	$2$	$10$	$2$
20.1.2b2	$2$	S	✓	$5$	$\Q(\sqrt{5}) $	20.1.2b	$C_5:C_4$	$C_5:C_4$	$20$	20.a1.a1	$1$	10.a1.a1	$2$	$10$	$2$
20.4.2a1	$2$	R		$5$	$\Q(\sqrt{5}) $	20.4.2a	$D_{10}$	$D_5$	$10$	10.a1.a1	$2$	10.a1.a1	$2$	$10$	$1$
20.4.2a2	$2$	R		$5$	$\Q(\sqrt{5}) $	20.4.2a	$D_{10}$	$D_5$	$10$	10.a1.a1	$2$	10.a1.a1	$2$	$10$	$1$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
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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
6.1.2a	$2$	R	✓	$1$	\(\Q\)	6.1.2a	$S_3$	$S_3$	$6$	6.a1.a1	$1$	6.a1.a1	$1$	$6$	$1$
8.3.2a	$2$	R	✓	$1$	\(\Q\)	8.3.2a	$D_4$	$D_4$	$8$	8.a1.a1	$1$	4.a1.a1	$2$	$4$	$1$
8.4.2a	$2$	S	✓	$1$	\(\Q\)	8.4.2a	$Q_8$	$Q_8$	$8$	8.a1.a1	$1$	4.a1.a1	$2$	$4$	$2$
10.1.2a1	$2$	R	✓	$5$	\(\Q(\sqrt{5}) \)	10.1.2a	$D_5$	$D_5$	$10$	10.a1.a1	$1$	10.a1.a1	$1$	$10$	$1$
10.1.2a2	$2$	R	✓	$5$	\(\Q(\sqrt{5}) \)	10.1.2a	$D_5$	$D_5$	$10$	10.a1.a1	$1$	10.a1.a1	$1$	$10$	$1$
12.1.2a	$2$	R		$1$	\(\Q\)	12.1.2a	$C_3:C_4$	$S_3$	$6$	6.a1.a1	$2$	6.a1.a1	$2$	$6$	$1$
12.1.2b	$2$	S	✓	$1$	\(\Q\)	12.1.2b	$C_3:C_4$	$C_3:C_4$	$12$	12.a1.a1	$1$	6.a1.a1	$2$	$6$	$2$
12.4.2a	$2$	R		$1$	\(\Q\)	12.4.2a	$D_6$	$S_3$	$6$	6.a1.a1	$2$	6.a1.a1	$2$	$6$	$1$
12.4.2b	$2$	R	✓	$1$	\(\Q\)	12.4.2b	$D_6$	$D_6$	$12$	12.a1.a1	$1$	6.a1.a1	$2$	$6$	$1$
14.1.2a1	$2$	R	✓	$7$	\(\Q(\zeta_{7})^+\)	14.1.2a	$D_7$	$D_7$	$14$	14.a1.a1	$1$	14.a1.a1	$1$	$14$	$1$
14.1.2a2	$2$	R	✓	$7$	\(\Q(\zeta_{7})^+\)	14.1.2a	$D_7$	$D_7$	$14$	14.a1.a1	$1$	14.a1.a1	$1$	$14$	$1$
14.1.2a3	$2$	R	✓	$7$	\(\Q(\zeta_{7})^+\)	14.1.2a	$D_7$	$D_7$	$14$	14.a1.a1	$1$	14.a1.a1	$1$	$14$	$1$
16.3.2a	$2$	R		$1$	\(\Q\)	16.3.2a	$C_2^2:C_4$	$D_4$	$8$	8.b1.b1	$2$	4.a1.a1	$4$	$4$	$1$
16.3.2b	$2$	R		$1$	\(\Q\)	16.3.2b	$C_2^2:C_4$	$D_4$	$8$	8.b1.a1	$2$	4.a1.a1	$4$	$4$	$1$
16.4.2a	$2$	R		$1$	\(\Q\)	16.4.2a	$C_4:C_4$	$D_4$	$8$	8.c1.a1	$2$	4.a1.a1	$4$	$4$	$1$
16.4.2b	$2$	S		$1$	\(\Q\)	16.4.2b	$C_4:C_4$	$Q_8$	$8$	8.a1.a1	$2$	4.a1.a1	$4$	$4$	$2$
16.6.2a1	$2$	C	✓	$4$	\(\Q(\sqrt{-1}) \)	16.6.2a	$\OD_{16}$	$\OD_{16}$	$16$	16.a1.a1	$1$	4.b1.a1	$4$	$4$	$1$
16.6.2a2	$2$	C	✓	$4$	\(\Q(\sqrt{-1}) \)	16.6.2a	$\OD_{16}$	$\OD_{16}$	$16$	16.a1.a1	$1$	4.b1.a1	$4$	$4$	$1$
16.7.2a	$2$	R		$1$	\(\Q\)	16.7.2a	$D_8$	$D_4$	$8$	8.a1.a1	$2$	4.a1.a1	$4$	$4$	$1$
16.7.2b1	$2$	R	✓	$8$	\(\Q(\sqrt{2}) \)	16.7.2b	$D_8$	$D_8$	$16$	16.a1.a1	$1$	8.a1.a1	$2$	$8$	$1$
16.7.2b2	$2$	R	✓	$8$	\(\Q(\sqrt{2}) \)	16.7.2b	$D_8$	$D_8$	$16$	16.a1.a1	$1$	8.a1.a1	$2$	$8$	$1$
16.8.2a	$2$	R		$1$	\(\Q\)	16.8.2a	$\SD_{16}$	$D_4$	$8$	8.a1.a1	$2$	4.a1.a1	$4$	$4$	$1$
16.8.2b1	$2$	C	✓	$8$	\(\Q(\sqrt{-2}) \)	16.8.2b	$\SD_{16}$	$\SD_{16}$	$16$	16.a1.a1	$1$	8.a1.a1	$2$	$8$	$1$
16.8.2b2	$2$	C	✓	$8$	\(\Q(\sqrt{-2}) \)	16.8.2b	$\SD_{16}$	$\SD_{16}$	$16$	16.a1.a1	$1$	8.a1.a1	$2$	$8$	$1$
16.9.2a	$2$	R		$1$	\(\Q\)	16.9.2a	$Q_{16}$	$D_4$	$8$	8.a1.a1	$2$	4.a1.a1	$4$	$4$	$1$
16.9.2b1	$2$	S	✓	$8$	\(\Q(\sqrt{2}) \)	16.9.2b	$Q_{16}$	$Q_{16}$	$16$	16.a1.a1	$1$	8.a1.a1	$2$	$8$	$2$
16.9.2b2	$2$	S	✓	$8$	\(\Q(\sqrt{2}) \)	16.9.2b	$Q_{16}$	$Q_{16}$	$16$	16.a1.a1	$1$	8.a1.a1	$2$	$8$	$2$
16.11.2a	$2$	R		$1$	\(\Q\)	16.11.2a	$C_2\times D_4$	$D_4$	$8$	8.a1.a1	$2$	4.a1.a1	$4$	$4$	$1$
16.11.2b	$2$	R		$1$	\(\Q\)	16.11.2b	$C_2\times D_4$	$D_4$	$8$	8.a1.b1	$2$	4.a1.a1	$4$	$4$	$1$
16.12.2a	$2$	S		$1$	\(\Q\)	16.12.2a	$C_2\times Q_8$	$Q_8$	$8$	8.a1.b1	$2$	4.a1.a1	$4$	$4$	$2$
16.12.2b	$2$	S		$1$	\(\Q\)	16.12.2b	$C_2\times Q_8$	$Q_8$	$8$	8.a1.a1	$2$	4.a1.a1	$4$	$4$	$2$
16.13.2a1	$2$	C	✓	$4$	\(\Q(\sqrt{-1}) \)	16.13.2a	$D_4:C_2$	$D_4:C_2$	$16$	16.a1.a1	$1$	4.b1.a1	$4$	$4$	$1$
16.13.2a2	$2$	C	✓	$4$	\(\Q(\sqrt{-1}) \)	16.13.2a	$D_4:C_2$	$D_4:C_2$	$16$	16.a1.a1	$1$	4.b1.a1	$4$	$4$	$1$
18.1.2a	$2$	R		$1$	\(\Q\)	18.1.2a	$D_9$	$S_3$	$6$	6.a1.a1	$3$	6.a1.a1	$3$	$6$	$1$
18.1.2b1	$2$	R	✓	$9$	\(\Q(\zeta_{9})^+\)	18.1.2b	$D_9$	$D_9$	$18$	18.a1.a1	$1$	18.a1.a1	$1$	$18$	$1$
18.1.2b2	$2$	R	✓	$9$	\(\Q(\zeta_{9})^+\)	18.1.2b	$D_9$	$D_9$	$18$	18.a1.a1	$1$	18.a1.a1	$1$	$18$	$1$
18.1.2b3	$2$	R	✓	$9$	\(\Q(\zeta_{9})^+\)	18.1.2b	$D_9$	$D_9$	$18$	18.a1.a1	$1$	18.a1.a1	$1$	$18$	$1$
18.3.2a	$2$	R		$1$	\(\Q\)	18.3.2a	$C_3\times S_3$	$S_3$	$6$	6.a1.a1	$3$	6.a1.a1	$3$	$6$	$1$
18.3.2b1	$2$	C	✓	$3$	\(\Q(\sqrt{-3}) \)	18.3.2b	$C_3\times S_3$	$C_3\times S_3$	$18$	18.a1.a1	$1$	6.a1.a1	$3$	$6$	$1$
18.3.2b2	$2$	C	✓	$3$	\(\Q(\sqrt{-3}) \)	18.3.2b	$C_3\times S_3$	$C_3\times S_3$	$18$	18.a1.a1	$1$	6.a1.a1	$3$	$6$	$1$
18.4.2a	$2$	R		$1$	\(\Q\)	18.4.2a	$C_3:S_3$	$S_3$	$6$	6.a1.d1	$3$	6.a1.d1	$3$	$6$	$1$
18.4.2b	$2$	R		$1$	\(\Q\)	18.4.2b	$C_3:S_3$	$S_3$	$6$	6.a1.c1	$3$	6.a1.c1	$3$	$6$	$1$
18.4.2c	$2$	R		$1$	\(\Q\)	18.4.2c	$C_3:S_3$	$S_3$	$6$	6.a1.b1	$3$	6.a1.b1	$3$	$6$	$1$
18.4.2d	$2$	R		$1$	\(\Q\)	18.4.2d	$C_3:S_3$	$S_3$	$6$	6.a1.a1	$3$	6.a1.a1	$3$	$6$	$1$
20.1.2a1	$2$	R		$5$	\(\Q(\sqrt{5}) \)	20.1.2a	$C_5:C_4$	$D_5$	$10$	10.a1.a1	$2$	10.a1.a1	$2$	$10$	$1$
20.1.2a2	$2$	R		$5$	\(\Q(\sqrt{5}) \)	20.1.2a	$C_5:C_4$	$D_5$	$10$	10.a1.a1	$2$	10.a1.a1	$2$	$10$	$1$
20.1.2b1	$2$	S	✓	$5$	\(\Q(\sqrt{5}) \)	20.1.2b	$C_5:C_4$	$C_5:C_4$	$20$	20.a1.a1	$1$	10.a1.a1	$2$	$10$	$2$
20.1.2b2	$2$	S	✓	$5$	\(\Q(\sqrt{5}) \)	20.1.2b	$C_5:C_4$	$C_5:C_4$	$20$	20.a1.a1	$1$	10.a1.a1	$2$	$10$	$2$
20.4.2a1	$2$	R		$5$	\(\Q(\sqrt{5}) \)	20.4.2a	$D_{10}$	$D_5$	$10$	10.a1.a1	$2$	10.a1.a1	$2$	$10$	$1$
20.4.2a2	$2$	R		$5$	\(\Q(\sqrt{5}) \)	20.4.2a	$D_{10}$	$D_5$	$10$	10.a1.a1	$2$	10.a1.a1	$2$	$10$	$1$