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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 (25 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	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4704.2.a.c	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots$
4704.2.a.d	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{9}+2q^{11}+2q^{15}+\cdots$
4704.2.a.f	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-1$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}-q^{11}+q^{15}+8q^{17}+\cdots$
4704.2.a.g	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}-2q^{11}+q^{13}-2q^{17}+\cdots$
4704.2.a.h	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}-2q^{11}+5q^{13}-2q^{17}+\cdots$
4704.2.a.j	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}+2q^{11}-q^{13}+2q^{17}+\cdots$
4704.2.a.k	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}+2q^{11}+2q^{13}-4q^{17}+\cdots$
4704.2.a.m	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots$
4704.2.a.o	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$3$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}+q^{9}+q^{11}-4q^{13}+\cdots$
4704.2.a.p	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$4$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{5}+q^{9}-6q^{11}-5q^{13}+\cdots$
4704.2.a.r	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}+q^{9}-6q^{11}+5q^{13}+\cdots$
4704.2.a.s	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-3$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}+q^{9}+q^{11}+4q^{13}+\cdots$
4704.2.a.u	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{9}-2q^{11}-2q^{15}+\cdots$
4704.2.a.x	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}-2q^{11}-5q^{13}+2q^{17}+\cdots$
4704.2.a.y	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}-2q^{11}-q^{13}+2q^{17}+\cdots$
4704.2.a.z	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}-2q^{11}+2q^{13}-4q^{17}+\cdots$
4704.2.a.ba	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}+2q^{11}+q^{13}-2q^{17}+\cdots$
4704.2.a.bc	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}-q^{11}+q^{15}-8q^{17}+\cdots$
4704.2.a.bi	$4704$	$2$	4704.a	1.a	$1$	$2$	$2$	$37.562$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$-2$	$0$	$0$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+q^{9}+\beta q^{11}-\beta q^{15}+\cdots$
4704.2.a.bj	$4704$	$2$	4704.a	1.a	$1$	$2$	$2$	$37.562$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$-2$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}+\beta q^{13}+\cdots$
4704.2.a.bn	$4704$	$2$	4704.a	1.a	$1$	$2$	$2$	$37.562$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$2$	$0$	$0$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+q^{9}+(-2-\beta )q^{11}+\cdots$
4704.2.a.bo	$4704$	$2$	4704.a	1.a	$1$	$2$	$2$	$37.562$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$2$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}-3\beta q^{13}+\cdots$
4704.2.a.bp	$4704$	$2$	4704.a	1.a	$1$	$2$	$2$	$37.562$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$2$	$0$	$0$	$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}-\beta q^{11}+\beta q^{13}+\beta q^{17}+\cdots$
4704.2.a.bw	$4704$	$2$	4704.a	1.a	$1$	$4$	$4$	$37.562$	4.4.2624.1	None	✓	$1$	$1$	$0$	$-4$	$-4$	$0$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta _{3})q^{5}+q^{9}+(1-\beta _{2}+\cdots)q^{11}+\cdots$
4704.2.a.by	$4704$	$2$	4704.a	1.a	$1$	$4$	$4$	$37.562$	4.4.2624.1	None	✓	$1$	$1$	$0$	$4$	$-4$	$0$	$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta _{3})q^{5}+q^{9}+(-1+\beta _{2}+\cdots)q^{11}+\cdots$

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Elliptic 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.