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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	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3136.2.a.a	$3136$	$2$	3136.a	1.a	$1$	$1$	$1$	$25.041$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$-1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}+6q^{9}-q^{11}+2q^{13}+\cdots$
3136.2.a.b	$3136$	$2$	3136.a	1.a	$1$	$1$	$1$	$25.041$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$1$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}+6q^{9}+q^{11}-2q^{13}+\cdots$
3136.2.a.c	$3136$	$2$	3136.a	1.a	$1$	$1$	$1$	$25.041$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$-4$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-4q^{5}+q^{9}+8q^{15}+2q^{17}+\cdots$
3136.2.a.f	$3136$	$2$	3136.a	1.a	$1$	$1$	$1$	$25.041$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}+4q^{11}-4q^{13}+2q^{17}+\cdots$
3136.2.a.h	$3136$	$2$	3136.a	1.a	$1$	$1$	$1$	$25.041$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-3$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}-2q^{9}+3q^{11}-2q^{13}+\cdots$
3136.2.a.k	$3136$	$2$	3136.a	1.a	$1$	$1$	$1$	$25.041$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$3$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}-2q^{9}-3q^{11}+2q^{13}+\cdots$
3136.2.a.l	$3136$	$2$	3136.a	1.a	$1$	$1$	$1$	$25.041$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$1$	$0$	$0$	$-4$	$0$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q-4q^{5}-3q^{9}+4q^{13}+8q^{17}+11q^{25}+\cdots$
3136.2.a.m	$3136$	$2$	3136.a	1.a	$1$	$1$	$1$	$25.041$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$1$	$0$	$0$	$-2$	$0$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{5}-3q^{9}+6q^{13}-2q^{17}-q^{25}+\cdots$
3136.2.a.o	$3136$	$2$	3136.a	1.a	$1$	$1$	$1$	$25.041$	$\Q$	$\Q(\sqrt{-7}) $	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q-3q^{9}+4q^{11}-8q^{23}-5q^{25}-2q^{29}+\cdots$
3136.2.a.p	$3136$	$2$	3136.a	1.a	$1$	$1$	$1$	$25.041$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-3q^{9}-4q^{11}+2q^{13}+6q^{17}+\cdots$
3136.2.a.r	$3136$	$2$	3136.a	1.a	$1$	$1$	$1$	$25.041$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$1$	$0$	$0$	$4$	$0$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q+4q^{5}-3q^{9}-4q^{13}-8q^{17}+11q^{25}+\cdots$
3136.2.a.t	$3136$	$2$	3136.a	1.a	$1$	$1$	$1$	$25.041$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{9}+3q^{11}-6q^{13}+\cdots$
3136.2.a.u	$3136$	$2$	3136.a	1.a	$1$	$1$	$1$	$25.041$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$1$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}-3q^{11}+6q^{13}+\cdots$
3136.2.a.y	$3136$	$2$	3136.a	1.a	$1$	$1$	$1$	$25.041$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}-4q^{11}-4q^{13}+2q^{17}+\cdots$
3136.2.a.z	$3136$	$2$	3136.a	1.a	$1$	$1$	$1$	$25.041$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}-4q^{13}-6q^{17}-2q^{19}+\cdots$
3136.2.a.bd	$3136$	$2$	3136.a	1.a	$1$	$2$	$2$	$25.041$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$-2$	$-2$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(-1+2\beta )q^{5}-2\beta q^{9}+\cdots$
3136.2.a.bg	$3136$	$2$	3136.a	1.a	$1$	$2$	$2$	$25.041$	$\Q(\sqrt{7}) $	None	✓	$2$	$1$	$0$	$0$	$-6$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-3q^{5}+4q^{9}+\beta q^{11}-4q^{13}+\cdots$
3136.2.a.bk	$3136$	$2$	3136.a	1.a	$1$	$2$	$2$	$25.041$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+2\beta q^{5}-q^{9}-6q^{11}-4\beta q^{13}+\cdots$
3136.2.a.bl	$3136$	$2$	3136.a	1.a	$1$	$2$	$2$	$25.041$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{9}-2q^{11}+2\beta q^{13}-3\beta q^{17}+\cdots$
3136.2.a.bn	$3136$	$2$	3136.a	1.a	$1$	$2$	$2$	$25.041$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2\beta q^{5}-q^{9}+2q^{11}-4q^{15}+\cdots$
3136.2.a.bo	$3136$	$2$	3136.a	1.a	$1$	$2$	$2$	$25.041$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{9}+2q^{11}-2\beta q^{13}+3\beta q^{17}+\cdots$
3136.2.a.bq	$3136$	$2$	3136.a	1.a	$1$	$2$	$2$	$25.041$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{5}+5q^{9}-4q^{11}+\beta q^{13}+\cdots$
3136.2.a.br	$3136$	$2$	3136.a	1.a	$1$	$2$	$2$	$25.041$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{3}-\beta q^{5}+5q^{9}-4q^{11}-3\beta q^{13}+\cdots$
3136.2.a.bu	$3136$	$2$	3136.a	1.a	$1$	$2$	$2$	$25.041$	$\Q(\sqrt{3}) $	None	✓	$2$	$1$	$0$	$0$	$2$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}-3\beta q^{11}+\beta q^{15}-5q^{17}+\cdots$
3136.2.a.bw	$3136$	$2$	3136.a	1.a	$1$	$2$	$2$	$25.041$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$2$	$-2$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-1-2\beta )q^{5}+2\beta q^{9}+\cdots$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
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.