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Note: Search results may be incomplete due to uncomputed quantities: fricke_eigenval (110727 objects)

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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 (36 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				A-L signs				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	5	37	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5550.2.a.a	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	$1$	$2$	$-1$	$-1$	$0$	$-4$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-4q^{7}-q^{8}+\cdots$
5550.2.a.f	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$0$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
5550.2.a.j	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$0$	$2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots$
5550.2.a.k	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$0$	$5$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+5q^{7}-q^{8}+\cdots$
5550.2.a.l	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$0$	$5$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+5q^{7}-q^{8}+\cdots$
5550.2.a.m	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$0$	$-3$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots$
5550.2.a.p	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$0$	$-2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots$
5550.2.a.r	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$0$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
5550.2.a.s	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$0$	$2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots$
5550.2.a.x	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$0$	$-2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots$
5550.2.a.ba	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$0$	$1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
5550.2.a.bd	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$0$	$4$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+4q^{7}+q^{8}+\cdots$
5550.2.a.bg	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$-3$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots$
5550.2.a.bk	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots$
5550.2.a.bn	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
5550.2.a.bo	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots$
5550.2.a.bp	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots$
5550.2.a.bq	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$4$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots$
5550.2.a.br	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$4$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots$
5550.2.a.bs	$5550$	$2$	5550.a	1.a	$1$	$2$	$2$	$44.317$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$-2$	$0$	$-2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+(-1+\beta )q^{7}+\cdots$
5550.2.a.bw	$5550$	$2$	5550.a	1.a	$1$	$2$	$2$	$44.317$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$-2$	$2$	$0$	$2$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots$
5550.2.a.bx	$5550$	$2$	5550.a	1.a	$1$	$2$	$2$	$44.317$	$\Q(\sqrt{113}) $	None	✓	$1$	$0$	$2$	$-2$	$0$	$-6$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-3q^{7}+q^{8}+\cdots$
5550.2.a.bz	$5550$	$2$	5550.a	1.a	$1$	$2$	$2$	$44.317$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$-2$	$0$	$4$	$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots$
5550.2.a.ca	$5550$	$2$	5550.a	1.a	$1$	$2$	$2$	$44.317$	$\Q(\sqrt{33}) $	None	✓	$1$	$0$	$2$	$2$	$0$	$1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+\beta q^{7}+q^{8}+\cdots$
5550.2.a.cc	$5550$	$2$	5550.a	1.a	$1$	$2$	$2$	$44.317$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$2$	$2$	$0$	$2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+(1+\beta )q^{7}+\cdots$
5550.2.a.cd	$5550$	$2$	5550.a	1.a	$1$	$3$	$3$	$44.317$	3.3.993.1	None	✓	$1$	$0$	$-3$	$-3$	$0$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+(\beta _{1}-\beta _{2})q^{7}+\cdots$
5550.2.a.ce	$5550$	$2$	5550.a	1.a	$1$	$3$	$3$	$44.317$	3.3.257.1	None	✓	$1$	$0$	$-3$	$3$	$0$	$-4$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
5550.2.a.cg	$5550$	$2$	5550.a	1.a	$1$	$3$	$3$	$44.317$	3.3.568.1	None	✓	$1$	$0$	$3$	$-3$	$0$	$-3$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
5550.2.a.ch	$5550$	$2$	5550.a	1.a	$1$	$3$	$3$	$44.317$	3.3.257.1	None	✓	$1$	$0$	$3$	$-3$	$0$	$4$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+(1+\beta _{1}-\beta _{2})q^{7}+\cdots$
5550.2.a.ci	$5550$	$2$	5550.a	1.a	$1$	$3$	$3$	$44.317$	3.3.993.1	None	✓	$1$	$0$	$3$	$3$	$0$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+(-\beta _{1}+\beta _{2})q^{7}+\cdots$
5550.2.a.cj	$5550$	$2$	5550.a	1.a	$1$	$4$	$4$	$44.317$	4.4.54764.1	None	✓	$1$	$0$	$-4$	$-4$	$0$	$-4$	$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
5550.2.a.ck	$5550$	$2$	5550.a	1.a	$1$	$4$	$4$	$44.317$	4.4.358377.1	None	✓	$1$	$0$	$-4$	$4$	$0$	$-4$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
5550.2.a.cl	$5550$	$2$	5550.a	1.a	$1$	$4$	$4$	$44.317$	4.4.30056.1	None	✓	$1$	$0$	$-4$	$4$	$0$	$3$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+(1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
5550.2.a.cn	$5550$	$2$	5550.a	1.a	$1$	$4$	$4$	$44.317$	4.4.358377.1	None	✓	$1$	$0$	$4$	$-4$	$0$	$4$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+(1+\beta _{1}+\beta _{3})q^{7}+\cdots$
5550.2.a.co	$5550$	$2$	5550.a	1.a	$1$	$5$	$5$	$44.317$	5.5.60594425.1	None	✓	$1$	$0$	$-5$	$-5$	$0$	$-2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-\beta _{4}q^{7}-q^{8}+\cdots$
5550.2.a.cp	$5550$	$2$	5550.a	1.a	$1$	$5$	$5$	$44.317$	5.5.60594425.1	None	✓	$1$	$0$	$5$	$5$	$0$	$2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+\beta _{4}q^{7}+q^{8}+\cdots$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
Higher genus families
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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.