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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 (22 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	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6840.2.a.b	$6840$	$2$	6840.a	1.a	$1$	$1$	$1$	$54.618$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$-2$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+2q^{11}-4q^{13}+2q^{17}+\cdots$
6840.2.a.c	$6840$	$2$	6840.a	1.a	$1$	$1$	$1$	$54.618$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}-4q^{11}+q^{13}+7q^{17}+\cdots$
6840.2.a.e	$6840$	$2$	6840.a	1.a	$1$	$1$	$1$	$54.618$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{11}+2q^{13}-6q^{17}-q^{19}+\cdots$
6840.2.a.f	$6840$	$2$	6840.a	1.a	$1$	$1$	$1$	$54.618$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{11}-q^{19}+4q^{23}+q^{25}+\cdots$
6840.2.a.j	$6840$	$2$	6840.a	1.a	$1$	$1$	$1$	$54.618$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-6q^{11}+4q^{13}+2q^{17}+\cdots$
6840.2.a.k	$6840$	$2$	6840.a	1.a	$1$	$1$	$1$	$54.618$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-2q^{13}-4q^{17}+q^{19}+\cdots$
6840.2.a.l	$6840$	$2$	6840.a	1.a	$1$	$1$	$1$	$54.618$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$4$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}-4q^{11}-4q^{13}+2q^{17}+\cdots$
6840.2.a.o	$6840$	$2$	6840.a	1.a	$1$	$1$	$1$	$54.618$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$4$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}+4q^{11}-6q^{17}-q^{19}+\cdots$
6840.2.a.s	$6840$	$2$	6840.a	1.a	$1$	$1$	$1$	$54.618$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{11}-q^{19}-4q^{23}+q^{25}+\cdots$
6840.2.a.t	$6840$	$2$	6840.a	1.a	$1$	$1$	$1$	$54.618$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+4q^{11}-2q^{13}+2q^{17}+q^{19}+\cdots$
6840.2.a.v	$6840$	$2$	6840.a	1.a	$1$	$2$	$2$	$54.618$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$0$	$-2$	$-6$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(-3+\beta )q^{7}+(1+3\beta )q^{11}+\cdots$
6840.2.a.w	$6840$	$2$	6840.a	1.a	$1$	$2$	$2$	$54.618$	$\Q(\sqrt{7}) $	None	✓	$1$	$1$	$0$	$0$	$-2$	$-2$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(-1+\beta )q^{7}+(3-\beta )q^{11}+(1+\cdots)q^{13}+\cdots$
6840.2.a.x	$6840$	$2$	6840.a	1.a	$1$	$2$	$2$	$54.618$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$0$	$2$	$-4$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(-2+\beta )q^{7}-\beta q^{11}-3\beta q^{13}+\cdots$
6840.2.a.y	$6840$	$2$	6840.a	1.a	$1$	$2$	$2$	$54.618$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{11}+(1+\beta )q^{13}+(-4+2\beta )q^{17}+\cdots$
6840.2.a.z	$6840$	$2$	6840.a	1.a	$1$	$2$	$2$	$54.618$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2\beta q^{7}+(-2-2\beta )q^{11}+(2+\cdots)q^{13}+\cdots$
6840.2.a.ba	$6840$	$2$	6840.a	1.a	$1$	$2$	$2$	$54.618$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{5}+\beta q^{7}+\beta q^{11}+(-2-\beta )q^{13}+\cdots$
6840.2.a.be	$6840$	$2$	6840.a	1.a	$1$	$3$	$3$	$54.618$	3.3.148.1	None	✓	$1$	$1$	$0$	$0$	$-3$	$-2$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(-2\beta _{1}-\beta _{2})q^{7}+(1-\beta _{1})q^{11}+\cdots$
6840.2.a.bg	$6840$	$2$	6840.a	1.a	$1$	$3$	$3$	$54.618$	3.3.229.1	None	✓	$1$	$1$	$0$	$0$	$-3$	$-1$	$+$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{5}+\beta _{1}q^{7}+(2+\beta _{2})q^{13}+(-2+\cdots)q^{17}+\cdots$
6840.2.a.bk	$6840$	$2$	6840.a	1.a	$1$	$3$	$3$	$54.618$	3.3.568.1	None	✓	$1$	$1$	$0$	$0$	$3$	$-2$	$-$	$-$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{5}+(-1-\beta _{2})q^{7}+(-1+\beta _{2})q^{11}+\cdots$
6840.2.a.bl	$6840$	$2$	6840.a	1.a	$1$	$3$	$3$	$54.618$	3.3.148.1	None	✓	$1$	$1$	$0$	$0$	$3$	$-2$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(-2\beta _{1}-\beta _{2})q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots$
6840.2.a.bp	$6840$	$2$	6840.a	1.a	$1$	$4$	$4$	$54.618$	4.4.20308.1	None	✓	$1$	$1$	$0$	$0$	$-4$	$-4$	$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{5}+(-1+\beta _{1})q^{7}+(1-\beta _{1}-\beta _{3})q^{11}+\cdots$
6840.2.a.bq	$6840$	$2$	6840.a	1.a	$1$	$4$	$4$	$54.618$	4.4.20308.1	None	✓	$1$	$1$	$0$	$0$	$4$	$-4$	$+$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{5}+(-1+\beta _{1})q^{7}+(-1+\beta _{1}+\beta _{3})q^{11}+\cdots$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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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.