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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	3	7	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1386.4.a.d	$1386$	$4$	1386.a	1.a	$1$	$1$	$1$	$81.777$	$\Q$	None	✓	$1$	$0$	$-2$	$0$	$-1$	$-7$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}-q^{5}-7q^{7}-8q^{8}+\cdots$
1386.4.a.e	$1386$	$4$	1386.a	1.a	$1$	$1$	$1$	$81.777$	$\Q$	None	✓	$1$	$0$	$-2$	$0$	$4$	$-7$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+4q^{5}-7q^{7}-8q^{8}+\cdots$
1386.4.a.i	$1386$	$4$	1386.a	1.a	$1$	$1$	$1$	$81.777$	$\Q$	None	✓	$1$	$0$	$2$	$0$	$-11$	$-7$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}-11q^{5}-7q^{7}+8q^{8}+\cdots$
1386.4.a.j	$1386$	$4$	1386.a	1.a	$1$	$1$	$1$	$81.777$	$\Q$	None	✓	$1$	$0$	$2$	$0$	$-2$	$-7$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}-2q^{5}-7q^{7}+8q^{8}+\cdots$
1386.4.a.m	$1386$	$4$	1386.a	1.a	$1$	$1$	$1$	$81.777$	$\Q$	None	✓	$1$	$0$	$2$	$0$	$14$	$-7$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+14q^{5}-7q^{7}+8q^{8}+\cdots$
1386.4.a.n	$1386$	$4$	1386.a	1.a	$1$	$1$	$1$	$81.777$	$\Q$	None	✓	$1$	$0$	$2$	$0$	$21$	$7$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+21q^{5}+7q^{7}+8q^{8}+\cdots$
1386.4.a.o	$1386$	$4$	1386.a	1.a	$1$	$2$	$2$	$81.777$	$\Q(\sqrt{193}) $	None	✓	$1$	$0$	$-4$	$0$	$-19$	$14$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+(-9-\beta )q^{5}+7q^{7}+\cdots$
1386.4.a.r	$1386$	$4$	1386.a	1.a	$1$	$2$	$2$	$81.777$	$\Q(\sqrt{793}) $	None	✓	$1$	$0$	$-4$	$0$	$3$	$-14$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+(1+\beta )q^{5}-7q^{7}-8q^{8}+\cdots$
1386.4.a.s	$1386$	$4$	1386.a	1.a	$1$	$2$	$2$	$81.777$	$\Q(\sqrt{57}) $	None	✓	$1$	$0$	$-4$	$0$	$17$	$-14$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+(10-3\beta )q^{5}-7q^{7}+\cdots$
1386.4.a.t	$1386$	$4$	1386.a	1.a	$1$	$2$	$2$	$81.777$	$\Q(\sqrt{89}) $	None	✓	$1$	$0$	$-4$	$0$	$17$	$14$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+(9-\beta )q^{5}+7q^{7}-8q^{8}+\cdots$
1386.4.a.v	$1386$	$4$	1386.a	1.a	$1$	$2$	$2$	$81.777$	$\Q(\sqrt{113}) $	None	✓	$1$	$0$	$4$	$0$	$-14$	$14$	$-$	$-$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+(-7-\beta )q^{5}+7q^{7}+\cdots$
1386.4.a.ba	$1386$	$4$	1386.a	1.a	$1$	$2$	$2$	$81.777$	$\Q(\sqrt{137}) $	None	✓	$1$	$0$	$4$	$0$	$7$	$14$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+(4-\beta )q^{5}+7q^{7}+8q^{8}+\cdots$
1386.4.a.bb	$1386$	$4$	1386.a	1.a	$1$	$2$	$2$	$81.777$	$\Q(\sqrt{193}) $	None	✓	$1$	$0$	$4$	$0$	$19$	$14$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+(10-\beta )q^{5}+7q^{7}+\cdots$
1386.4.a.bd	$1386$	$4$	1386.a	1.a	$1$	$3$	$3$	$81.777$	3.3.843032.1	None	✓	$1$	$0$	$-6$	$0$	$-13$	$21$	$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+(-4-\beta _{1})q^{5}+7q^{7}+\cdots$
1386.4.a.bf	$1386$	$4$	1386.a	1.a	$1$	$3$	$3$	$81.777$	3.3.195128.1	None	✓	$1$	$0$	$-6$	$0$	$11$	$21$	$+$	$+$	$-$	$-$	$+$	$3^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+(4+\beta _{2})q^{5}+7q^{7}+\cdots$
1386.4.a.bg	$1386$	$4$	1386.a	1.a	$1$	$3$	$3$	$81.777$	3.3.195128.1	None	✓	$1$	$0$	$6$	$0$	$-11$	$21$	$-$	$+$	$-$	$+$	$+$	$3^{2}$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+(-4-\beta _{2})q^{5}+7q^{7}+\cdots$
1386.4.a.bh	$1386$	$4$	1386.a	1.a	$1$	$3$	$3$	$81.777$	3.3.1028796.1	None	✓	$1$	$0$	$6$	$0$	$-7$	$-21$	$-$	$-$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+(-2-\beta _{1})q^{5}-7q^{7}+\cdots$
1386.4.a.bi	$1386$	$4$	1386.a	1.a	$1$	$3$	$3$	$81.777$	3.3.768425.1	None	✓	$1$	$0$	$6$	$0$	$7$	$21$	$-$	$-$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+(2-\beta _{1})q^{5}+7q^{7}+\cdots$
1386.4.a.bk	$1386$	$4$	1386.a	1.a	$1$	$4$	$4$	$81.777$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$0$	$-8$	$0$	$-18$	$-28$	$+$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+(-4+\beta _{2})q^{5}-7q^{7}+\cdots$
1386.4.a.bl	$1386$	$4$	1386.a	1.a	$1$	$4$	$4$	$81.777$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$0$	$8$	$0$	$18$	$-28$	$-$	$+$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+(4-\beta _{2})q^{5}-7q^{7}+\cdots$

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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.