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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 (24 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	17	23	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8993.2.a.a	$8993$	$2$	8993.a	1.a	$1$	$1$	$1$	$71.809$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$2$	$-4$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+2q^{5}-4q^{7}+3q^{8}-3q^{9}+\cdots$
8993.2.a.b	$8993$	$2$	8993.a	1.a	$1$	$2$	$2$	$71.809$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-1$	$2$	$2$	$2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(2-2\beta )q^{5}+\cdots$
8993.2.a.c	$8993$	$2$	8993.a	1.a	$1$	$3$	$3$	$71.809$	3.3.257.1	None	✓	$1$	$1$	$-1$	$-6$	$3$	$-1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-2q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots$
8993.2.a.d	$8993$	$2$	8993.a	1.a	$1$	$3$	$3$	$71.809$	3.3.169.1	None	✓	$1$	$0$	$-1$	$0$	$1$	$5$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
8993.2.a.e	$8993$	$2$	8993.a	1.a	$1$	$4$	$4$	$71.809$	4.4.7537.1	None	✓	$1$	$0$	$1$	$4$	$-3$	$1$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
8993.2.a.f	$8993$	$2$	8993.a	1.a	$1$	$4$	$4$	$71.809$	4.4.7537.1	None	✓	$1$	$1$	$1$	$4$	$3$	$-1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
8993.2.a.g	$8993$	$2$	8993.a	1.a	$1$	$9$	$9$	$71.809$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$2$	$2$	$-7$	$-3$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
8993.2.a.h	$8993$	$2$	8993.a	1.a	$1$	$11$	$11$	$71.809$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$1$	$-1$	$-5$	$-5$	$-12$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$
8993.2.a.i	$8993$	$2$	8993.a	1.a	$1$	$11$	$11$	$71.809$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$-1$	$-5$	$5$	$12$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots$
8993.2.a.j	$8993$	$2$	8993.a	1.a	$1$	$12$	$12$	$71.809$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$4$	$2$	$-5$	$9$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots$
8993.2.a.k	$8993$	$2$	8993.a	1.a	$1$	$14$	$14$	$71.809$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$1$	$0$	$-2$	$-2$	$-8$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{11}q^{3}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots$
8993.2.a.l	$8993$	$2$	8993.a	1.a	$1$	$14$	$14$	$71.809$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$0$	$-2$	$2$	$8$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{11}q^{3}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots$
8993.2.a.m	$8993$	$2$	8993.a	1.a	$1$	$15$	$15$	$71.809$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$1$	$0$	$-1$	$-2$	$-5$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{7}+\beta _{8})q^{4}+\cdots$
8993.2.a.n	$8993$	$2$	8993.a	1.a	$1$	$15$	$15$	$71.809$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$0$	$0$	$-1$	$2$	$5$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{7}+\beta _{8})q^{4}+\cdots$
8993.2.a.o	$8993$	$2$	8993.a	1.a	$1$	$28$	$28$	$71.809$		None	✓	$1$	$1$	$0$	$4$	$-4$	$-20$	$+$	$+$	$+$		$\mathrm{SU}(2)$
8993.2.a.p	$8993$	$2$	8993.a	1.a	$1$	$28$	$28$	$71.809$		None	✓	$1$	$0$	$0$	$4$	$4$	$20$	$-$	$+$	$-$		$\mathrm{SU}(2)$
8993.2.a.q	$8993$	$2$	8993.a	1.a	$1$	$30$	$30$	$71.809$		None	✓	$1$	$1$	$0$	$-2$	$-4$	$-22$	$-$	$-$	$+$		$\mathrm{SU}(2)$
8993.2.a.r	$8993$	$2$	8993.a	1.a	$1$	$30$	$30$	$71.809$		None	✓	$1$	$0$	$0$	$-2$	$4$	$22$	$+$	$-$	$-$		$\mathrm{SU}(2)$
8993.2.a.s	$8993$	$2$	8993.a	1.a	$1$	$60$	$60$	$71.809$		None	✓	$1$	$1$	$0$	$4$	$-8$	$-40$	$+$	$+$	$+$		$\mathrm{SU}(2)$
8993.2.a.t	$8993$	$2$	8993.a	1.a	$1$	$60$	$60$	$71.809$		None	✓	$1$	$0$	$0$	$4$	$8$	$40$	$-$	$+$	$-$		$\mathrm{SU}(2)$
8993.2.a.u	$8993$	$2$	8993.a	1.a	$1$	$70$	$70$	$71.809$		None	✓	$1$	$1$	$-11$	$-21$	$-10$	$-10$	$-$	$-$	$+$		$\mathrm{SU}(2)$
8993.2.a.v	$8993$	$2$	8993.a	1.a	$1$	$70$	$70$	$71.809$		None	✓	$1$	$1$	$-11$	$-21$	$10$	$10$	$+$	$+$	$+$		$\mathrm{SU}(2)$
8993.2.a.w	$8993$	$2$	8993.a	1.a	$1$	$90$	$90$	$71.809$		None	✓	$1$	$0$	$9$	$19$	$-8$	$-10$	$+$	$-$	$-$		$\mathrm{SU}(2)$
8993.2.a.x	$8993$	$2$	8993.a	1.a	$1$	$90$	$90$	$71.809$		None	✓	$1$	$0$	$9$	$19$	$8$	$10$	$-$	$+$	$-$		$\mathrm{SU}(2)$

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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.