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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 (19 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
3528.2.a.a	$3528$	$2$	3528.a	1.a	$1$	$1$	$1$	$28.171$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-4$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-3q^{13}+4q^{17}+7q^{19}-4q^{23}+\cdots$
3528.2.a.c	$3528$	$2$	3528.a	1.a	$1$	$1$	$1$	$28.171$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-4$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+3q^{13}+4q^{17}-7q^{19}+4q^{23}+\cdots$
3528.2.a.d	$3528$	$2$	3528.a	1.a	$1$	$1$	$1$	$28.171$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{11}+2q^{13}+2q^{17}+4q^{19}+\cdots$
3528.2.a.e	$3528$	$2$	3528.a	1.a	$1$	$1$	$1$	$28.171$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+2q^{11}-2q^{13}-6q^{17}+4q^{19}+\cdots$
3528.2.a.f	$3528$	$2$	3528.a	1.a	$1$	$1$	$1$	$28.171$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+6q^{11}-3q^{13}-4q^{17}-5q^{19}+\cdots$
3528.2.a.k	$3528$	$2$	3528.a	1.a	$1$	$1$	$1$	$28.171$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{11}-2q^{13}+3q^{17}-5q^{19}+\cdots$
3528.2.a.m	$3528$	$2$	3528.a	1.a	$1$	$1$	$1$	$28.171$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{13}+4q^{17}+4q^{19}-4q^{23}+\cdots$
3528.2.a.n	$3528$	$2$	3528.a	1.a	$1$	$1$	$1$	$28.171$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{13}-4q^{17}-4q^{19}-4q^{23}+\cdots$
3528.2.a.o	$3528$	$2$	3528.a	1.a	$1$	$1$	$1$	$28.171$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-5q^{11}+2q^{13}-6q^{17}+2q^{19}+\cdots$
3528.2.a.p	$3528$	$2$	3528.a	1.a	$1$	$1$	$1$	$28.171$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{11}-6q^{13}+5q^{17}+q^{19}+\cdots$
3528.2.a.q	$3528$	$2$	3528.a	1.a	$1$	$1$	$1$	$28.171$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{11}+4q^{13}-4q^{19}-8q^{23}+\cdots$
3528.2.a.s	$3528$	$2$	3528.a	1.a	$1$	$1$	$1$	$28.171$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+5q^{11}-2q^{13}-6q^{17}-2q^{19}+\cdots$
3528.2.a.t	$3528$	$2$	3528.a	1.a	$1$	$1$	$1$	$28.171$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-6q^{11}+6q^{13}-2q^{17}-4q^{19}+\cdots$
3528.2.a.x	$3528$	$2$	3528.a	1.a	$1$	$1$	$1$	$28.171$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+4q^{11}-2q^{13}-6q^{17}-8q^{19}+\cdots$
3528.2.a.bb	$3528$	$2$	3528.a	1.a	$1$	$2$	$2$	$28.171$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$0$	$-4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{5}+(-2+2\beta )q^{11}-\beta q^{13}+\cdots$
3528.2.a.bd	$3528$	$2$	3528.a	1.a	$1$	$2$	$2$	$28.171$	$\Q(\sqrt{57}) $	None	✓	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{5}+\beta q^{11}+(-3+\beta )q^{13}-4q^{17}+\cdots$
3528.2.a.bf	$3528$	$2$	3528.a	1.a	$1$	$2$	$2$	$28.171$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}-2q^{11}-2\beta q^{13}+\beta q^{17}+\cdots$
3528.2.a.bg	$3528$	$2$	3528.a	1.a	$1$	$2$	$2$	$28.171$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-\beta q^{13}-\beta q^{17}-4q^{23}-3q^{25}+\cdots$
3528.2.a.bl	$3528$	$2$	3528.a	1.a	$1$	$2$	$2$	$28.171$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$0$	$4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}+(-2-2\beta )q^{11}-\beta q^{13}+\cdots$

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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.