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
3.1.1b1	$1$	C	✓	$3$	$\Q(\sqrt{-3}) $	3.1.1b	$C_3$	$C_3$	$3$	3.a1.a1	$1$	1.a1.a1	$3$	$1$	$1$
3.1.1b2	$1$	C	✓	$3$	$\Q(\sqrt{-3}) $	3.1.1b	$C_3$	$C_3$	$3$	3.a1.a1	$1$	1.a1.a1	$3$	$1$	$1$
4.1.1c1	$1$	C	✓	$4$	$\Q(\sqrt{-1}) $	4.1.1c	$C_4$	$C_4$	$4$	4.a1.a1	$1$	1.a1.a1	$4$	$1$	$1$
4.1.1c2	$1$	C	✓	$4$	$\Q(\sqrt{-1}) $	4.1.1c	$C_4$	$C_4$	$4$	4.a1.a1	$1$	1.a1.a1	$4$	$1$	$1$
5.1.1b1	$1$	C	✓	$5$	$\Q(\zeta_{5})$	5.1.1b	$C_5$	$C_5$	$5$	5.a1.a1	$1$	1.a1.a1	$5$	$1$	$1$
5.1.1b2	$1$	C	✓	$5$	$\Q(\zeta_{5})$	5.1.1b	$C_5$	$C_5$	$5$	5.a1.a1	$1$	1.a1.a1	$5$	$1$	$1$
5.1.1b3	$1$	C	✓	$5$	$\Q(\zeta_{5})$	5.1.1b	$C_5$	$C_5$	$5$	5.a1.a1	$1$	1.a1.a1	$5$	$1$	$1$
5.1.1b4	$1$	C	✓	$5$	$\Q(\zeta_{5})$	5.1.1b	$C_5$	$C_5$	$5$	5.a1.a1	$1$	1.a1.a1	$5$	$1$	$1$
6.2.1c1	$1$	C		$3$	$\Q(\sqrt{-3}) $	6.2.1c	$C_6$	$C_3$	$3$	3.a1.a1	$2$	1.a1.a1	$6$	$1$	$1$
6.2.1c2	$1$	C		$3$	$\Q(\sqrt{-3}) $	6.2.1c	$C_6$	$C_3$	$3$	3.a1.a1	$2$	1.a1.a1	$6$	$1$	$1$
6.2.1d1	$1$	C	✓	$3$	$\Q(\sqrt{-3}) $	6.2.1d	$C_6$	$C_6$	$6$	6.a1.a1	$1$	1.a1.a1	$6$	$1$	$1$
6.2.1d2	$1$	C	✓	$3$	$\Q(\sqrt{-3}) $	6.2.1d	$C_6$	$C_6$	$6$	6.a1.a1	$1$	1.a1.a1	$6$	$1$	$1$
7.1.1b1	$1$	C	✓	$7$	$\Q(\zeta_{7})$	7.1.1b	$C_7$	$C_7$	$7$	7.a1.a1	$1$	1.a1.a1	$7$	$1$	$1$
7.1.1b2	$1$	C	✓	$7$	$\Q(\zeta_{7})$	7.1.1b	$C_7$	$C_7$	$7$	7.a1.a1	$1$	1.a1.a1	$7$	$1$	$1$
7.1.1b3	$1$	C	✓	$7$	$\Q(\zeta_{7})$	7.1.1b	$C_7$	$C_7$	$7$	7.a1.a1	$1$	1.a1.a1	$7$	$1$	$1$
7.1.1b4	$1$	C	✓	$7$	$\Q(\zeta_{7})$	7.1.1b	$C_7$	$C_7$	$7$	7.a1.a1	$1$	1.a1.a1	$7$	$1$	$1$
7.1.1b5	$1$	C	✓	$7$	$\Q(\zeta_{7})$	7.1.1b	$C_7$	$C_7$	$7$	7.a1.a1	$1$	1.a1.a1	$7$	$1$	$1$
7.1.1b6	$1$	C	✓	$7$	$\Q(\zeta_{7})$	7.1.1b	$C_7$	$C_7$	$7$	7.a1.a1	$1$	1.a1.a1	$7$	$1$	$1$
8.1.1c1	$1$	C		$4$	$\Q(\sqrt{-1}) $	8.1.1c	$C_8$	$C_4$	$4$	4.a1.a1	$2$	1.a1.a1	$8$	$1$	$1$
8.1.1c2	$1$	C		$4$	$\Q(\sqrt{-1}) $	8.1.1c	$C_8$	$C_4$	$4$	4.a1.a1	$2$	1.a1.a1	$8$	$1$	$1$
8.1.1d1	$1$	C	✓	$8$	$\Q(\zeta_{8})$	8.1.1d	$C_8$	$C_8$	$8$	8.a1.a1	$1$	1.a1.a1	$8$	$1$	$1$
8.1.1d2	$1$	C	✓	$8$	$\Q(\zeta_{8})$	8.1.1d	$C_8$	$C_8$	$8$	8.a1.a1	$1$	1.a1.a1	$8$	$1$	$1$
8.1.1d3	$1$	C	✓	$8$	$\Q(\zeta_{8})$	8.1.1d	$C_8$	$C_8$	$8$	8.a1.a1	$1$	1.a1.a1	$8$	$1$	$1$
8.1.1d4	$1$	C	✓	$8$	$\Q(\zeta_{8})$	8.1.1d	$C_8$	$C_8$	$8$	8.a1.a1	$1$	1.a1.a1	$8$	$1$	$1$
8.2.1e1	$1$	C		$4$	$\Q(\sqrt{-1}) $	8.2.1e	$C_2\times C_4$	$C_4$	$4$	4.a1.a1	$2$	1.a1.a1	$8$	$1$	$1$
8.2.1e2	$1$	C		$4$	$\Q(\sqrt{-1}) $	8.2.1e	$C_2\times C_4$	$C_4$	$4$	4.a1.a1	$2$	1.a1.a1	$8$	$1$	$1$
8.2.1f1	$1$	C		$4$	$\Q(\sqrt{-1}) $	8.2.1f	$C_2\times C_4$	$C_4$	$4$	4.a1.b1	$2$	1.a1.a1	$8$	$1$	$1$
8.2.1f2	$1$	C		$4$	$\Q(\sqrt{-1}) $	8.2.1f	$C_2\times C_4$	$C_4$	$4$	4.a1.b1	$2$	1.a1.a1	$8$	$1$	$1$
9.1.1b1	$1$	C		$3$	$\Q(\sqrt{-3}) $	9.1.1b	$C_9$	$C_3$	$3$	3.a1.a1	$3$	1.a1.a1	$9$	$1$	$1$
9.1.1b2	$1$	C		$3$	$\Q(\sqrt{-3}) $	9.1.1b	$C_9$	$C_3$	$3$	3.a1.a1	$3$	1.a1.a1	$9$	$1$	$1$
9.1.1c1	$1$	C	✓	$9$	$\Q(\zeta_{9})$	9.1.1c	$C_9$	$C_9$	$9$	9.a1.a1	$1$	1.a1.a1	$9$	$1$	$1$
9.1.1c2	$1$	C	✓	$9$	$\Q(\zeta_{9})$	9.1.1c	$C_9$	$C_9$	$9$	9.a1.a1	$1$	1.a1.a1	$9$	$1$	$1$
9.1.1c3	$1$	C	✓	$9$	$\Q(\zeta_{9})$	9.1.1c	$C_9$	$C_9$	$9$	9.a1.a1	$1$	1.a1.a1	$9$	$1$	$1$
9.1.1c4	$1$	C	✓	$9$	$\Q(\zeta_{9})$	9.1.1c	$C_9$	$C_9$	$9$	9.a1.a1	$1$	1.a1.a1	$9$	$1$	$1$
9.1.1c5	$1$	C	✓	$9$	$\Q(\zeta_{9})$	9.1.1c	$C_9$	$C_9$	$9$	9.a1.a1	$1$	1.a1.a1	$9$	$1$	$1$
9.1.1c6	$1$	C	✓	$9$	$\Q(\zeta_{9})$	9.1.1c	$C_9$	$C_9$	$9$	9.a1.a1	$1$	1.a1.a1	$9$	$1$	$1$
9.2.1b1	$1$	C		$3$	$\Q(\sqrt{-3}) $	9.2.1b	$C_3^2$	$C_3$	$3$	3.a1.c1	$3$	1.a1.a1	$9$	$1$	$1$
9.2.1b2	$1$	C		$3$	$\Q(\sqrt{-3}) $	9.2.1b	$C_3^2$	$C_3$	$3$	3.a1.c1	$3$	1.a1.a1	$9$	$1$	$1$
9.2.1c1	$1$	C		$3$	$\Q(\sqrt{-3}) $	9.2.1c	$C_3^2$	$C_3$	$3$	3.a1.d1	$3$	1.a1.a1	$9$	$1$	$1$
9.2.1c2	$1$	C		$3$	$\Q(\sqrt{-3}) $	9.2.1c	$C_3^2$	$C_3$	$3$	3.a1.d1	$3$	1.a1.a1	$9$	$1$	$1$
9.2.1d1	$1$	C		$3$	$\Q(\sqrt{-3}) $	9.2.1d	$C_3^2$	$C_3$	$3$	3.a1.a1	$3$	1.a1.a1	$9$	$1$	$1$
9.2.1d2	$1$	C		$3$	$\Q(\sqrt{-3}) $	9.2.1d	$C_3^2$	$C_3$	$3$	3.a1.a1	$3$	1.a1.a1	$9$	$1$	$1$
9.2.1e1	$1$	C		$3$	$\Q(\sqrt{-3}) $	9.2.1e	$C_3^2$	$C_3$	$3$	3.a1.b1	$3$	1.a1.a1	$9$	$1$	$1$
9.2.1e2	$1$	C		$3$	$\Q(\sqrt{-3}) $	9.2.1e	$C_3^2$	$C_3$	$3$	3.a1.b1	$3$	1.a1.a1	$9$	$1$	$1$
10.2.1c1	$1$	C		$5$	$\Q(\zeta_{5})$	10.2.1c	$C_{10}$	$C_5$	$5$	5.a1.a1	$2$	1.a1.a1	$10$	$1$	$1$
10.2.1c2	$1$	C		$5$	$\Q(\zeta_{5})$	10.2.1c	$C_{10}$	$C_5$	$5$	5.a1.a1	$2$	1.a1.a1	$10$	$1$	$1$
10.2.1c3	$1$	C		$5$	$\Q(\zeta_{5})$	10.2.1c	$C_{10}$	$C_5$	$5$	5.a1.a1	$2$	1.a1.a1	$10$	$1$	$1$
10.2.1c4	$1$	C		$5$	$\Q(\zeta_{5})$	10.2.1c	$C_{10}$	$C_5$	$5$	5.a1.a1	$2$	1.a1.a1	$10$	$1$	$1$
10.2.1d1	$1$	C	✓	$5$	$\Q(\zeta_{5})$	10.2.1d	$C_{10}$	$C_{10}$	$10$	10.a1.a1	$1$	1.a1.a1	$10$	$1$	$1$
10.2.1d2	$1$	C	✓	$5$	$\Q(\zeta_{5})$	10.2.1d	$C_{10}$	$C_{10}$	$10$	10.a1.a1	$1$	1.a1.a1	$10$	$1$	$1$

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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
3.1.1b1	$1$	C	✓	$3$	\(\Q(\sqrt{-3}) \)	3.1.1b	$C_3$	$C_3$	$3$	3.a1.a1	$1$	1.a1.a1	$3$	$1$	$1$
3.1.1b2	$1$	C	✓	$3$	\(\Q(\sqrt{-3}) \)	3.1.1b	$C_3$	$C_3$	$3$	3.a1.a1	$1$	1.a1.a1	$3$	$1$	$1$
4.1.1c1	$1$	C	✓	$4$	\(\Q(\sqrt{-1}) \)	4.1.1c	$C_4$	$C_4$	$4$	4.a1.a1	$1$	1.a1.a1	$4$	$1$	$1$
4.1.1c2	$1$	C	✓	$4$	\(\Q(\sqrt{-1}) \)	4.1.1c	$C_4$	$C_4$	$4$	4.a1.a1	$1$	1.a1.a1	$4$	$1$	$1$
5.1.1b1	$1$	C	✓	$5$	\(\Q(\zeta_{5})\)	5.1.1b	$C_5$	$C_5$	$5$	5.a1.a1	$1$	1.a1.a1	$5$	$1$	$1$
5.1.1b2	$1$	C	✓	$5$	\(\Q(\zeta_{5})\)	5.1.1b	$C_5$	$C_5$	$5$	5.a1.a1	$1$	1.a1.a1	$5$	$1$	$1$
5.1.1b3	$1$	C	✓	$5$	\(\Q(\zeta_{5})\)	5.1.1b	$C_5$	$C_5$	$5$	5.a1.a1	$1$	1.a1.a1	$5$	$1$	$1$
5.1.1b4	$1$	C	✓	$5$	\(\Q(\zeta_{5})\)	5.1.1b	$C_5$	$C_5$	$5$	5.a1.a1	$1$	1.a1.a1	$5$	$1$	$1$
6.2.1c1	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	6.2.1c	$C_6$	$C_3$	$3$	3.a1.a1	$2$	1.a1.a1	$6$	$1$	$1$
6.2.1c2	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	6.2.1c	$C_6$	$C_3$	$3$	3.a1.a1	$2$	1.a1.a1	$6$	$1$	$1$
6.2.1d1	$1$	C	✓	$3$	\(\Q(\sqrt{-3}) \)	6.2.1d	$C_6$	$C_6$	$6$	6.a1.a1	$1$	1.a1.a1	$6$	$1$	$1$
6.2.1d2	$1$	C	✓	$3$	\(\Q(\sqrt{-3}) \)	6.2.1d	$C_6$	$C_6$	$6$	6.a1.a1	$1$	1.a1.a1	$6$	$1$	$1$
7.1.1b1	$1$	C	✓	$7$	\(\Q(\zeta_{7})\)	7.1.1b	$C_7$	$C_7$	$7$	7.a1.a1	$1$	1.a1.a1	$7$	$1$	$1$
7.1.1b2	$1$	C	✓	$7$	\(\Q(\zeta_{7})\)	7.1.1b	$C_7$	$C_7$	$7$	7.a1.a1	$1$	1.a1.a1	$7$	$1$	$1$
7.1.1b3	$1$	C	✓	$7$	\(\Q(\zeta_{7})\)	7.1.1b	$C_7$	$C_7$	$7$	7.a1.a1	$1$	1.a1.a1	$7$	$1$	$1$
7.1.1b4	$1$	C	✓	$7$	\(\Q(\zeta_{7})\)	7.1.1b	$C_7$	$C_7$	$7$	7.a1.a1	$1$	1.a1.a1	$7$	$1$	$1$
7.1.1b5	$1$	C	✓	$7$	\(\Q(\zeta_{7})\)	7.1.1b	$C_7$	$C_7$	$7$	7.a1.a1	$1$	1.a1.a1	$7$	$1$	$1$
7.1.1b6	$1$	C	✓	$7$	\(\Q(\zeta_{7})\)	7.1.1b	$C_7$	$C_7$	$7$	7.a1.a1	$1$	1.a1.a1	$7$	$1$	$1$
8.1.1c1	$1$	C		$4$	\(\Q(\sqrt{-1}) \)	8.1.1c	$C_8$	$C_4$	$4$	4.a1.a1	$2$	1.a1.a1	$8$	$1$	$1$
8.1.1c2	$1$	C		$4$	\(\Q(\sqrt{-1}) \)	8.1.1c	$C_8$	$C_4$	$4$	4.a1.a1	$2$	1.a1.a1	$8$	$1$	$1$
8.1.1d1	$1$	C	✓	$8$	\(\Q(\zeta_{8})\)	8.1.1d	$C_8$	$C_8$	$8$	8.a1.a1	$1$	1.a1.a1	$8$	$1$	$1$
8.1.1d2	$1$	C	✓	$8$	\(\Q(\zeta_{8})\)	8.1.1d	$C_8$	$C_8$	$8$	8.a1.a1	$1$	1.a1.a1	$8$	$1$	$1$
8.1.1d3	$1$	C	✓	$8$	\(\Q(\zeta_{8})\)	8.1.1d	$C_8$	$C_8$	$8$	8.a1.a1	$1$	1.a1.a1	$8$	$1$	$1$
8.1.1d4	$1$	C	✓	$8$	\(\Q(\zeta_{8})\)	8.1.1d	$C_8$	$C_8$	$8$	8.a1.a1	$1$	1.a1.a1	$8$	$1$	$1$
8.2.1e1	$1$	C		$4$	\(\Q(\sqrt{-1}) \)	8.2.1e	$C_2\times C_4$	$C_4$	$4$	4.a1.a1	$2$	1.a1.a1	$8$	$1$	$1$
8.2.1e2	$1$	C		$4$	\(\Q(\sqrt{-1}) \)	8.2.1e	$C_2\times C_4$	$C_4$	$4$	4.a1.a1	$2$	1.a1.a1	$8$	$1$	$1$
8.2.1f1	$1$	C		$4$	\(\Q(\sqrt{-1}) \)	8.2.1f	$C_2\times C_4$	$C_4$	$4$	4.a1.b1	$2$	1.a1.a1	$8$	$1$	$1$
8.2.1f2	$1$	C		$4$	\(\Q(\sqrt{-1}) \)	8.2.1f	$C_2\times C_4$	$C_4$	$4$	4.a1.b1	$2$	1.a1.a1	$8$	$1$	$1$
9.1.1b1	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	9.1.1b	$C_9$	$C_3$	$3$	3.a1.a1	$3$	1.a1.a1	$9$	$1$	$1$
9.1.1b2	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	9.1.1b	$C_9$	$C_3$	$3$	3.a1.a1	$3$	1.a1.a1	$9$	$1$	$1$
9.1.1c1	$1$	C	✓	$9$	\(\Q(\zeta_{9})\)	9.1.1c	$C_9$	$C_9$	$9$	9.a1.a1	$1$	1.a1.a1	$9$	$1$	$1$
9.1.1c2	$1$	C	✓	$9$	\(\Q(\zeta_{9})\)	9.1.1c	$C_9$	$C_9$	$9$	9.a1.a1	$1$	1.a1.a1	$9$	$1$	$1$
9.1.1c3	$1$	C	✓	$9$	\(\Q(\zeta_{9})\)	9.1.1c	$C_9$	$C_9$	$9$	9.a1.a1	$1$	1.a1.a1	$9$	$1$	$1$
9.1.1c4	$1$	C	✓	$9$	\(\Q(\zeta_{9})\)	9.1.1c	$C_9$	$C_9$	$9$	9.a1.a1	$1$	1.a1.a1	$9$	$1$	$1$
9.1.1c5	$1$	C	✓	$9$	\(\Q(\zeta_{9})\)	9.1.1c	$C_9$	$C_9$	$9$	9.a1.a1	$1$	1.a1.a1	$9$	$1$	$1$
9.1.1c6	$1$	C	✓	$9$	\(\Q(\zeta_{9})\)	9.1.1c	$C_9$	$C_9$	$9$	9.a1.a1	$1$	1.a1.a1	$9$	$1$	$1$
9.2.1b1	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	9.2.1b	$C_3^2$	$C_3$	$3$	3.a1.c1	$3$	1.a1.a1	$9$	$1$	$1$
9.2.1b2	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	9.2.1b	$C_3^2$	$C_3$	$3$	3.a1.c1	$3$	1.a1.a1	$9$	$1$	$1$
9.2.1c1	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	9.2.1c	$C_3^2$	$C_3$	$3$	3.a1.d1	$3$	1.a1.a1	$9$	$1$	$1$
9.2.1c2	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	9.2.1c	$C_3^2$	$C_3$	$3$	3.a1.d1	$3$	1.a1.a1	$9$	$1$	$1$
9.2.1d1	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	9.2.1d	$C_3^2$	$C_3$	$3$	3.a1.a1	$3$	1.a1.a1	$9$	$1$	$1$
9.2.1d2	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	9.2.1d	$C_3^2$	$C_3$	$3$	3.a1.a1	$3$	1.a1.a1	$9$	$1$	$1$
9.2.1e1	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	9.2.1e	$C_3^2$	$C_3$	$3$	3.a1.b1	$3$	1.a1.a1	$9$	$1$	$1$
9.2.1e2	$1$	C		$3$	\(\Q(\sqrt{-3}) \)	9.2.1e	$C_3^2$	$C_3$	$3$	3.a1.b1	$3$	1.a1.a1	$9$	$1$	$1$
10.2.1c1	$1$	C		$5$	\(\Q(\zeta_{5})\)	10.2.1c	$C_{10}$	$C_5$	$5$	5.a1.a1	$2$	1.a1.a1	$10$	$1$	$1$
10.2.1c2	$1$	C		$5$	\(\Q(\zeta_{5})\)	10.2.1c	$C_{10}$	$C_5$	$5$	5.a1.a1	$2$	1.a1.a1	$10$	$1$	$1$
10.2.1c3	$1$	C		$5$	\(\Q(\zeta_{5})\)	10.2.1c	$C_{10}$	$C_5$	$5$	5.a1.a1	$2$	1.a1.a1	$10$	$1$	$1$
10.2.1c4	$1$	C		$5$	\(\Q(\zeta_{5})\)	10.2.1c	$C_{10}$	$C_5$	$5$	5.a1.a1	$2$	1.a1.a1	$10$	$1$	$1$
10.2.1d1	$1$	C	✓	$5$	\(\Q(\zeta_{5})\)	10.2.1d	$C_{10}$	$C_{10}$	$10$	10.a1.a1	$1$	1.a1.a1	$10$	$1$	$1$
10.2.1d2	$1$	C	✓	$5$	\(\Q(\zeta_{5})\)	10.2.1d	$C_{10}$	$C_{10}$	$10$	10.a1.a1	$1$	1.a1.a1	$10$	$1$	$1$