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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	17	29	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8381.2.a.a	$8381$	$2$	8381.a	1.a	$1$	$1$	$1$	$66.923$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$2$	$5$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+2q^{5}+5q^{7}+3q^{8}-3q^{9}+\cdots$
8381.2.a.b	$8381$	$2$	8381.a	1.a	$1$	$1$	$1$	$66.923$	$\Q$	None	✓	$1$	$1$	$-1$	$3$	$-1$	$2$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}-q^{4}-q^{5}-3q^{6}+2q^{7}+\cdots$
8381.2.a.c	$8381$	$2$	8381.a	1.a	$1$	$1$	$1$	$66.923$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$-1$	$-1$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{4}-q^{5}-q^{7}+q^{9}+2q^{11}+\cdots$
8381.2.a.d	$8381$	$2$	8381.a	1.a	$1$	$1$	$1$	$66.923$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$1$	$1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{4}+q^{5}+q^{7}+q^{9}-2q^{11}+\cdots$
8381.2.a.e	$8381$	$2$	8381.a	1.a	$1$	$2$	$2$	$66.923$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$-2$	$-2$	$2$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-2\beta )q^{4}+\cdots$
8381.2.a.f	$8381$	$2$	8381.a	1.a	$1$	$2$	$2$	$66.923$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$2$	$1$	$-3$	$-5$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta )q^{3}-q^{4}+(-1-\beta )q^{5}+\cdots$
8381.2.a.g	$8381$	$2$	8381.a	1.a	$1$	$4$	$4$	$66.923$	4.4.8468.1	None	✓	$1$	$0$	$2$	$-3$	$-3$	$-1$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{2})q^{2}+(-1-\beta _{3})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots$
8381.2.a.h	$8381$	$2$	8381.a	1.a	$1$	$5$	$5$	$66.923$	5.5.270017.1	None	✓	$1$	$1$	$-2$	$2$	$1$	$4$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots$
8381.2.a.i	$8381$	$2$	8381.a	1.a	$1$	$6$	$6$	$66.923$	6.6.7313969.1	None	✓	$1$	$0$	$5$	$-2$	$-1$	$-2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
8381.2.a.j	$8381$	$2$	8381.a	1.a	$1$	$8$	$8$	$66.923$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$3$	$-6$	$-1$	$-3$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
8381.2.a.k	$8381$	$2$	8381.a	1.a	$1$	$10$	$10$	$66.923$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$-5$	$9$	$4$	$4$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{6}q^{2}+(1-\beta _{1})q^{3}+(1+\beta _{3}-\beta _{6}+\cdots)q^{4}+\cdots$
8381.2.a.l	$8381$	$2$	8381.a	1.a	$1$	$14$	$14$	$66.923$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$1$	$-1$	$-3$	$0$	$2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots$
8381.2.a.m	$8381$	$2$	8381.a	1.a	$1$	$14$	$14$	$66.923$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$1$	$-1$	$3$	$0$	$-2$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{11}q^{3}+(1+\beta _{2})q^{4}-\beta _{12}q^{5}+\cdots$
8381.2.a.n	$8381$	$2$	8381.a	1.a	$1$	$21$	$21$	$66.923$		None	✓	$1$	$1$	$1$	$-6$	$-4$	$-8$	$+$	$+$	$+$		$\mathrm{SU}(2)$
8381.2.a.o	$8381$	$2$	8381.a	1.a	$1$	$21$	$21$	$66.923$		None	✓	$1$	$0$	$1$	$-1$	$1$	$3$	$-$	$+$	$-$		$\mathrm{SU}(2)$
8381.2.a.p	$8381$	$2$	8381.a	1.a	$1$	$21$	$21$	$66.923$		None	✓	$1$	$0$	$1$	$1$	$-1$	$-3$	$+$	$-$	$-$		$\mathrm{SU}(2)$
8381.2.a.q	$8381$	$2$	8381.a	1.a	$1$	$21$	$21$	$66.923$		None	✓	$1$	$0$	$1$	$6$	$4$	$8$	$+$	$-$	$-$		$\mathrm{SU}(2)$
8381.2.a.r	$8381$	$2$	8381.a	1.a	$1$	$42$	$42$	$66.923$		None	✓	$1$	$1$	$2$	$-12$	$-8$	$-16$	$+$	$+$	$+$		$\mathrm{SU}(2)$
8381.2.a.s	$8381$	$2$	8381.a	1.a	$1$	$42$	$42$	$66.923$		None	✓	$1$	$0$	$2$	$12$	$8$	$16$	$+$	$-$	$-$		$\mathrm{SU}(2)$
8381.2.a.t	$8381$	$2$	8381.a	1.a	$1$	$48$	$48$	$66.923$		None	✓	$1$	$1$	$-3$	$-3$	$0$	$0$	$-$	$-$	$+$		$\mathrm{SU}(2)$
8381.2.a.u	$8381$	$2$	8381.a	1.a	$1$	$48$	$48$	$66.923$		None	✓	$1$	$1$	$-3$	$3$	$0$	$0$	$+$	$+$	$+$		$\mathrm{SU}(2)$
8381.2.a.v	$8381$	$2$	8381.a	1.a	$1$	$66$	$66$	$66.923$		None	✓	$1$	$0$	$3$	$-3$	$0$	$0$	$-$	$+$	$-$		$\mathrm{SU}(2)$
8381.2.a.w	$8381$	$2$	8381.a	1.a	$1$	$66$	$66$	$66.923$		None	✓	$1$	$0$	$3$	$3$	$0$	$0$	$+$	$-$	$-$		$\mathrm{SU}(2)$
8381.2.a.x	$8381$	$2$	8381.a	1.a	$1$	$84$	$84$	$66.923$		None	✓	$1$	$1$	$-4$	$-24$	$-16$	$-32$	$-$	$-$	$+$		$\mathrm{SU}(2)$
8381.2.a.y	$8381$	$2$	8381.a	1.a	$1$	$84$	$84$	$66.923$		None	✓	$1$	$0$	$-4$	$24$	$16$	$32$	$-$	$+$	$-$		$\mathrm{SU}(2)$

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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.