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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (30 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
264.1.p.a	$264$	$1$	264.p	264.p	$2$	$1$	$1$	$0.132$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-66}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
264.1.p.b	$264$	$1$	264.p	264.p	$2$	$1$	$1$	$0.132$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-66}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
363.1.b.a	$363$	$1$	363.b	3.b	$2$	$1$	$1$	$0.181$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-11}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{4}+q^{9}-q^{12}+q^{16}+q^{25}+\cdots$
363.1.h.a	$363$	$1$	363.h	33.h	$10$	$4$	$1$	$0.181$	$\Q(\zeta_{10})$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-11}) $	$\Q(\sqrt{33}) $		$16$	$0$	$0$	$1$	$0$	$0$	$1$		$q-\zeta_{10}^{4}q^{3}-\zeta_{10}q^{4}-\zeta_{10}^{3}q^{9}-q^{12}+\cdots$
792.1.e.a	$792$	$1$	792.e	88.b	$2$	$1$	$1$	$0.395$	$\Q$	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-22}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+q^{11}+q^{16}-q^{22}+\cdots$
792.1.e.b	$792$	$1$	792.e	88.b	$2$	$1$	$1$	$0.395$	$\Q$	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-22}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}-q^{11}+q^{16}-q^{22}+\cdots$
1056.1.p.a	$1056$	$1$	1056.p	264.p	$2$	$1$	$1$	$0.527$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-66}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{9}-q^{11}+2q^{17}-q^{25}+\cdots$
1056.1.p.b	$1056$	$1$	1056.p	264.p	$2$	$1$	$1$	$0.527$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-66}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{9}+q^{11}-2q^{17}-q^{25}+\cdots$
1221.1.j.a	$1221$	$1$	1221.j	1221.j	$4$	$2$	$1$	$0.609$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{33}) $		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+(-1-i)q^{2}+iq^{3}+iq^{4}+(1-i+\cdots)q^{6}+\cdots$
1221.1.j.d	$1221$	$1$	1221.j	1221.j	$4$	$2$	$1$	$0.609$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{33}) $		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+(1+i)q^{2}+iq^{3}+iq^{4}+(-1+i+\cdots)q^{6}+\cdots$
1683.1.b.a	$1683$	$1$	1683.b	187.b	$2$	$1$	$1$	$0.840$	$\Q$	$D_{2}$	$\Q(\sqrt{-51}) $, $\Q(\sqrt{-187}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}-q^{11}+q^{16}+q^{17}+q^{25}+\cdots$
1683.1.b.b	$1683$	$1$	1683.b	187.b	$2$	$1$	$1$	$0.840$	$\Q$	$D_{2}$	$\Q(\sqrt{-51}) $, $\Q(\sqrt{-187}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{11}+q^{16}-q^{17}+q^{25}+\cdots$
2244.1.k.a	$2244$	$1$	2244.k	2244.k	$2$	$1$	$1$	$1.120$	$\Q$	$D_{2}$	$\Q(\sqrt{-17}) $, $\Q(\sqrt{-561}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
2244.1.k.b	$2244$	$1$	2244.k	2244.k	$2$	$1$	$1$	$1.120$	$\Q$	$D_{2}$	$\Q(\sqrt{-17}) $, $\Q(\sqrt{-561}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
2244.1.k.c	$2244$	$1$	2244.k	2244.k	$2$	$1$	$1$	$1.120$	$\Q$	$D_{2}$	$\Q(\sqrt{-17}) $, $\Q(\sqrt{-561}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
2244.1.k.d	$2244$	$1$	2244.k	2244.k	$2$	$1$	$1$	$1.120$	$\Q$	$D_{2}$	$\Q(\sqrt{-17}) $, $\Q(\sqrt{-561}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$1$	$1$	$0$	$0$	$1$		$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
2739.1.e.a	$2739$	$1$	2739.e	2739.e	$2$	$1$	$1$	$1.367$	$\Q$	$D_{2}$	$\Q(\sqrt{-83}) $, $\Q(\sqrt{-2739}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{4}+q^{9}-q^{11}+q^{12}+q^{16}+\cdots$
2739.1.e.b	$2739$	$1$	2739.e	2739.e	$2$	$1$	$1$	$1.367$	$\Q$	$D_{2}$	$\Q(\sqrt{-83}) $, $\Q(\sqrt{-2739}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{4}+q^{9}+q^{11}+q^{12}+q^{16}+\cdots$
2871.1.h.a	$2871$	$1$	2871.h	319.d	$2$	$1$	$1$	$1.433$	$\Q$	$D_{2}$	$\Q(\sqrt{-87}) $, $\Q(\sqrt{-319}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-2q^{2}+3q^{4}-4q^{8}+q^{11}+5q^{16}+\cdots$
2871.1.h.b	$2871$	$1$	2871.h	319.d	$2$	$1$	$1$	$1.433$	$\Q$	$D_{2}$	$\Q(\sqrt{-87}) $, $\Q(\sqrt{-319}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+2q^{2}+3q^{4}+4q^{8}-q^{11}+5q^{16}+\cdots$
2904.1.r.b	$2904$	$1$	2904.r	264.r	$10$	$4$	$1$	$1.449$	$\Q(\zeta_{10})$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-66}) $	$\Q(\sqrt{33}) $		$16$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}^{4}q^{3}-\zeta_{10}q^{4}-\zeta_{10}^{2}q^{6}+\cdots$
2904.1.r.f	$2904$	$1$	2904.r	264.r	$10$	$4$	$1$	$1.449$	$\Q(\zeta_{10})$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-66}) $	$\Q(\sqrt{33}) $		$16$	$0$	$1$	$1$	$0$	$0$	$1$		$q+\zeta_{10}^{3}q^{2}-\zeta_{10}^{4}q^{3}-\zeta_{10}q^{4}+\zeta_{10}^{2}q^{6}+\cdots$
3168.1.e.a	$3168$	$1$	3168.e	88.b	$2$	$1$	$1$	$1.581$	$\Q$	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-22}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{11}+q^{25}+2q^{29}+2q^{31}+q^{49}+\cdots$
3168.1.e.b	$3168$	$1$	3168.e	88.b	$2$	$1$	$1$	$1.581$	$\Q$	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-22}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{11}+q^{25}-2q^{29}+2q^{31}+q^{49}+\cdots$
3531.1.e.a	$3531$	$1$	3531.e	3531.e	$2$	$1$	$1$	$1.762$	$\Q$	$D_{2}$	$\Q(\sqrt{-107}) $, $\Q(\sqrt{-3531}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{4}+q^{9}-q^{11}+q^{12}+q^{16}+\cdots$
3531.1.e.b	$3531$	$1$	3531.e	3531.e	$2$	$1$	$1$	$1.762$	$\Q$	$D_{2}$	$\Q(\sqrt{-107}) $, $\Q(\sqrt{-3531}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{4}+q^{9}+q^{11}+q^{12}+q^{16}+\cdots$
3828.1.f.a	$3828$	$1$	3828.f	3828.f	$2$	$1$	$1$	$1.910$	$\Q$	$D_{2}$	$\Q(\sqrt{-29}) $, $\Q(\sqrt{-957}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
3828.1.f.b	$3828$	$1$	3828.f	3828.f	$2$	$1$	$1$	$1.910$	$\Q$	$D_{2}$	$\Q(\sqrt{-29}) $, $\Q(\sqrt{-957}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
3828.1.f.c	$3828$	$1$	3828.f	3828.f	$2$	$1$	$1$	$1.910$	$\Q$	$D_{2}$	$\Q(\sqrt{-29}) $, $\Q(\sqrt{-957}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
3828.1.f.d	$3828$	$1$	3828.f	3828.f	$2$	$1$	$1$	$1.910$	$\Q$	$D_{2}$	$\Q(\sqrt{-29}) $, $\Q(\sqrt{-957}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$1$	$1$	$0$	$0$	$1$		$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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.