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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 (20 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	5	11	43	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4730.2.a.b	$4730$	$2$	4730.a	1.a	$1$	$1$	$1$	$37.769$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}-3q^{9}+q^{10}+\cdots$
4730.2.a.c	$4730$	$2$	4730.a	1.a	$1$	$1$	$1$	$37.769$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$1$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-3q^{9}-q^{10}+\cdots$
4730.2.a.d	$4730$	$2$	4730.a	1.a	$1$	$1$	$1$	$37.769$	$\Q$	None	✓	$1$	$1$	$1$	$-3$	$1$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}+q^{5}-3q^{6}+q^{7}+\cdots$
4730.2.a.e	$4730$	$2$	4730.a	1.a	$1$	$1$	$1$	$37.769$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$-1$	$-2$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-2q^{7}+\cdots$
4730.2.a.f	$4730$	$2$	4730.a	1.a	$1$	$1$	$1$	$37.769$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-1$	$3$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+3q^{7}+q^{8}-3q^{9}+\cdots$
4730.2.a.h	$4730$	$2$	4730.a	1.a	$1$	$1$	$1$	$37.769$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-1$	$2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots$
4730.2.a.i	$4730$	$2$	4730.a	1.a	$1$	$1$	$1$	$37.769$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$1$	$-3$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-3q^{7}+\cdots$
4730.2.a.l	$4730$	$2$	4730.a	1.a	$1$	$2$	$2$	$37.769$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$-2$	$-1$	$2$	$-6$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-3q^{7}+\cdots$
4730.2.a.m	$4730$	$2$	4730.a	1.a	$1$	$2$	$2$	$37.769$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$-2$	$-1$	$2$	$-2$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-2\beta q^{7}+\cdots$
4730.2.a.n	$4730$	$2$	4730.a	1.a	$1$	$2$	$2$	$37.769$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$-2$	$0$	$-2$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}-\beta q^{7}+\cdots$
4730.2.a.o	$4730$	$2$	4730.a	1.a	$1$	$2$	$2$	$37.769$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$-2$	$1$	$-2$	$-1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}-\beta q^{7}+\cdots$
4730.2.a.p	$4730$	$2$	4730.a	1.a	$1$	$2$	$2$	$37.769$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$2$	$-2$	$-2$	$-2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots$
4730.2.a.q	$4730$	$2$	4730.a	1.a	$1$	$2$	$2$	$37.769$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-1$	$2$	$-3$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+(-2+\cdots)q^{7}+\cdots$
4730.2.a.r	$4730$	$2$	4730.a	1.a	$1$	$2$	$2$	$37.769$	$\Q(\sqrt{21}) $	None	✓	$1$	$1$	$2$	$1$	$-2$	$-5$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(-2+\cdots)q^{7}+\cdots$
4730.2.a.s	$4730$	$2$	4730.a	1.a	$1$	$2$	$2$	$37.769$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$1$	$2$	$-5$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+(-2+\cdots)q^{7}+\cdots$
4730.2.a.t	$4730$	$2$	4730.a	1.a	$1$	$3$	$3$	$37.769$	3.3.1373.1	None	✓	$1$	$1$	$-3$	$0$	$3$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
4730.2.a.u	$4730$	$2$	4730.a	1.a	$1$	$4$	$4$	$37.769$	4.4.23252.1	None	✓	$1$	$1$	$4$	$-3$	$4$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots$
4730.2.a.v	$4730$	$2$	4730.a	1.a	$1$	$5$	$5$	$37.769$	5.5.220036.1	None	✓	$1$	$1$	$5$	$2$	$-5$	$-6$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
4730.2.a.w	$4730$	$2$	4730.a	1.a	$1$	$8$	$8$	$37.769$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-8$	$-7$	$8$	$-6$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots$
4730.2.a.x	$4730$	$2$	4730.a	1.a	$1$	$8$	$8$	$37.769$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-8$	$0$	$-8$	$-5$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$

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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.