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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	5	11	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9295.2.a.f	$9295$	$2$	9295.a	1.a	$1$	$2$	$2$	$74.221$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-3$	$-3$	$-2$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots$
9295.2.a.h	$9295$	$2$	9295.a	1.a	$1$	$2$	$2$	$74.221$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$0$	$-2$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+\beta q^{3}-q^{5}+2q^{6}+(2+\beta )q^{7}+\cdots$
9295.2.a.i	$9295$	$2$	9295.a	1.a	$1$	$2$	$2$	$74.221$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$3$	$-3$	$2$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots$
9295.2.a.j	$9295$	$2$	9295.a	1.a	$1$	$3$	$3$	$74.221$	3.3.148.1	None	✓	$1$	$1$	$-2$	$0$	$3$	$4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
9295.2.a.l	$9295$	$2$	9295.a	1.a	$1$	$4$	$4$	$74.221$	4.4.4752.1	None	✓	$1$	$1$	$-2$	$-2$	$4$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
9295.2.a.m	$9295$	$2$	9295.a	1.a	$1$	$4$	$4$	$74.221$	4.4.4752.1	None	✓	$1$	$1$	$2$	$-2$	$-4$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots$
9295.2.a.n	$9295$	$2$	9295.a	1.a	$1$	$6$	$6$	$74.221$	6.6.37261816.1	None	✓	$1$	$1$	$1$	$-4$	$6$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
9295.2.a.p	$9295$	$2$	9295.a	1.a	$1$	$8$	$8$	$74.221$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-4$	$0$	$8$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
9295.2.a.q	$9295$	$2$	9295.a	1.a	$1$	$8$	$8$	$74.221$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-2$	$0$	$-8$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
9295.2.a.r	$9295$	$2$	9295.a	1.a	$1$	$8$	$8$	$74.221$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$4$	$0$	$-8$	$1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
9295.2.a.s	$9295$	$2$	9295.a	1.a	$1$	$9$	$9$	$74.221$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$-1$	$0$	$9$	$-4$	$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
9295.2.a.u	$9295$	$2$	9295.a	1.a	$1$	$9$	$9$	$74.221$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$1$	$0$	$-9$	$4$	$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
9295.2.a.v	$9295$	$2$	9295.a	1.a	$1$	$10$	$10$	$74.221$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-1$	$-3$	$10$	$-3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
9295.2.a.w	$9295$	$2$	9295.a	1.a	$1$	$10$	$10$	$74.221$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$1$	$-3$	$-10$	$3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
9295.2.a.bd	$9295$	$2$	9295.a	1.a	$1$	$16$	$16$	$74.221$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$1$	$0$	$0$	$-16$	$10$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{11}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
9295.2.a.be	$9295$	$2$	9295.a	1.a	$1$	$16$	$16$	$74.221$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$1$	$0$	$0$	$16$	$-10$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{11}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
9295.2.a.bf	$9295$	$2$	9295.a	1.a	$1$	$27$	$27$	$74.221$		None	✓	$1$	$1$	$-10$	$-12$	$27$	$-8$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
9295.2.a.bg	$9295$	$2$	9295.a	1.a	$1$	$27$	$27$	$74.221$		None	✓	$1$	$1$	$-8$	$0$	$-27$	$-6$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
9295.2.a.bl	$9295$	$2$	9295.a	1.a	$1$	$33$	$33$	$74.221$		None	✓	$1$	$1$	$-10$	$0$	$33$	$-6$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
9295.2.a.bm	$9295$	$2$	9295.a	1.a	$1$	$33$	$33$	$74.221$		None	✓	$1$	$1$	$-8$	$12$	$-33$	$-4$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
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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.