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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 (45 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	11	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6171.2.a.a	$6171$	$2$	6171.a	1.a	$1$	$1$	$1$	$49.276$	$\Q$	None	✓	$1$	$1$	$-2$	$1$	$2$	$-3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}+2q^{5}-2q^{6}+\cdots$
6171.2.a.b	$6171$	$2$	6171.a	1.a	$1$	$1$	$1$	$49.276$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}+2q^{7}+3q^{8}+\cdots$
6171.2.a.c	$6171$	$2$	6171.a	1.a	$1$	$1$	$1$	$49.276$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-2$	$3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-2q^{5}+3q^{7}+q^{9}+2q^{12}+\cdots$
6171.2.a.d	$6171$	$2$	6171.a	1.a	$1$	$1$	$1$	$49.276$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-2$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-2q^{5}-q^{7}+q^{9}-2q^{12}+\cdots$
6171.2.a.e	$6171$	$2$	6171.a	1.a	$1$	$1$	$1$	$49.276$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$3$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+3q^{5}+4q^{7}+q^{9}-2q^{12}+\cdots$
6171.2.a.f	$6171$	$2$	6171.a	1.a	$1$	$1$	$1$	$49.276$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-2q^{7}-3q^{8}+\cdots$
6171.2.a.g	$6171$	$2$	6171.a	1.a	$1$	$1$	$1$	$49.276$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+2q^{5}+q^{6}-3q^{8}+\cdots$
6171.2.a.h	$6171$	$2$	6171.a	1.a	$1$	$1$	$1$	$49.276$	$\Q$	None	✓	$1$	$0$	$2$	$1$	$0$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+2q^{6}+3q^{7}+\cdots$
6171.2.a.i	$6171$	$2$	6171.a	1.a	$1$	$1$	$1$	$49.276$	$\Q$	None	✓	$1$	$0$	$2$	$1$	$2$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+2q^{5}+2q^{6}+\cdots$
6171.2.a.j	$6171$	$2$	6171.a	1.a	$1$	$2$	$2$	$49.276$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-1$	$-2$	$-6$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}-3q^{5}+\cdots$
6171.2.a.k	$6171$	$2$	6171.a	1.a	$1$	$2$	$2$	$49.276$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$-1$	$-2$	$4$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+2q^{5}+\beta q^{6}+\cdots$
6171.2.a.l	$6171$	$2$	6171.a	1.a	$1$	$2$	$2$	$49.276$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-2$	$1$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{2}-q^{3}+3q^{4}+(1-\beta )q^{5}+\cdots$
6171.2.a.m	$6171$	$2$	6171.a	1.a	$1$	$2$	$2$	$49.276$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-2$	$1$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{2}-q^{3}+3q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots$
6171.2.a.n	$6171$	$2$	6171.a	1.a	$1$	$2$	$2$	$49.276$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$2$	$-4$	$6$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(-2+\beta )q^{5}+\beta q^{6}+\cdots$
6171.2.a.o	$6171$	$2$	6171.a	1.a	$1$	$2$	$2$	$49.276$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$1$	$-2$	$-6$	$4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-3q^{5}+\cdots$
6171.2.a.p	$6171$	$2$	6171.a	1.a	$1$	$2$	$2$	$49.276$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$1$	$-2$	$3$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(2+\beta )q^{4}+(1+\beta )q^{5}+\cdots$
6171.2.a.q	$6171$	$2$	6171.a	1.a	$1$	$3$	$3$	$49.276$	3.3.316.1	None	✓	$1$	$0$	$-1$	$-3$	$4$	$-2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
6171.2.a.r	$6171$	$2$	6171.a	1.a	$1$	$3$	$3$	$49.276$	3.3.148.1	None	✓	$1$	$0$	$0$	$-3$	$-4$	$7$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots$
6171.2.a.s	$6171$	$2$	6171.a	1.a	$1$	$3$	$3$	$49.276$	3.3.148.1	None	✓	$1$	$1$	$2$	$-3$	$-2$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
6171.2.a.t	$6171$	$2$	6171.a	1.a	$1$	$4$	$4$	$49.276$	4.4.22676.1	None	✓	$1$	$1$	$-1$	$4$	$-4$	$-9$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots$
6171.2.a.u	$6171$	$2$	6171.a	1.a	$1$	$5$	$5$	$49.276$	5.5.749264.1	None	✓	$1$	$1$	$-2$	$5$	$0$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
6171.2.a.v	$6171$	$2$	6171.a	1.a	$1$	$5$	$5$	$49.276$	5.5.749264.1	None	✓	$1$	$0$	$2$	$5$	$0$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
6171.2.a.w	$6171$	$2$	6171.a	1.a	$1$	$6$	$6$	$49.276$	6.6.46051664.1	None	✓	$1$	$0$	$-1$	$-6$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
6171.2.a.x	$6171$	$2$	6171.a	1.a	$1$	$6$	$6$	$49.276$	6.6.29995216.1	None	✓	$1$	$0$	$-1$	$-6$	$0$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{3}-\beta _{4})q^{4}-\beta _{3}q^{5}+\cdots$
6171.2.a.y	$6171$	$2$	6171.a	1.a	$1$	$6$	$6$	$49.276$	6.6.4642000.1	None	✓	$1$	$1$	$-1$	$6$	$-2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
6171.2.a.z	$6171$	$2$	6171.a	1.a	$1$	$6$	$6$	$49.276$	6.6.29995216.1	None	✓	$1$	$1$	$1$	$-6$	$0$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{3}-\beta _{4})q^{4}-\beta _{3}q^{5}+\cdots$
6171.2.a.ba	$6171$	$2$	6171.a	1.a	$1$	$6$	$6$	$49.276$	6.6.46051664.1	None	✓	$1$	$1$	$1$	$-6$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
6171.2.a.bb	$6171$	$2$	6171.a	1.a	$1$	$6$	$6$	$49.276$	6.6.4642000.1	None	✓	$1$	$0$	$1$	$6$	$-2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
6171.2.a.bc	$6171$	$2$	6171.a	1.a	$1$	$6$	$6$	$49.276$	6.6.78067472.1	None	✓	$1$	$0$	$1$	$6$	$2$	$-7$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots$
6171.2.a.bd	$6171$	$2$	6171.a	1.a	$1$	$7$	$7$	$49.276$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$-3$	$7$	$0$	$-3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots$
6171.2.a.be	$6171$	$2$	6171.a	1.a	$1$	$7$	$7$	$49.276$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$3$	$7$	$0$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots$
6171.2.a.bf	$6171$	$2$	6171.a	1.a	$1$	$8$	$8$	$49.276$	8.8.$\cdots$.1	None	✓	$1$	$1$	$-4$	$-8$	$-5$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}-q^{3}+(-1+\beta _{3}-\beta _{5})q^{4}+\cdots$
6171.2.a.bg	$6171$	$2$	6171.a	1.a	$1$	$8$	$8$	$49.276$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$-1$	$-8$	$0$	$3$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots$
6171.2.a.bh	$6171$	$2$	6171.a	1.a	$1$	$8$	$8$	$49.276$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$1$	$-8$	$0$	$-3$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots$
6171.2.a.bi	$6171$	$2$	6171.a	1.a	$1$	$8$	$8$	$49.276$	8.8.$\cdots$.1	None	✓	$1$	$1$	$4$	$-8$	$-5$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}-q^{3}+(-1+\beta _{3}-\beta _{5})q^{4}+\cdots$
6171.2.a.bj	$6171$	$2$	6171.a	1.a	$1$	$12$	$12$	$49.276$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$-6$	$12$	$0$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
6171.2.a.bk	$6171$	$2$	6171.a	1.a	$1$	$12$	$12$	$49.276$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$-1$	$12$	$-14$	$-5$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{3}+\beta _{7}+\beta _{9}+\cdots)q^{4}+\cdots$
6171.2.a.bl	$6171$	$2$	6171.a	1.a	$1$	$12$	$12$	$49.276$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$1$	$12$	$-14$	$5$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{3}+\beta _{7}+\beta _{9}+\cdots)q^{4}+\cdots$
6171.2.a.bm	$6171$	$2$	6171.a	1.a	$1$	$12$	$12$	$49.276$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$6$	$12$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
6171.2.a.bn	$6171$	$2$	6171.a	1.a	$1$	$14$	$14$	$49.276$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$-2$	$-14$	$0$	$6$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots$
6171.2.a.bo	$6171$	$2$	6171.a	1.a	$1$	$14$	$14$	$49.276$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$1$	$2$	$-14$	$0$	$-6$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots$
6171.2.a.bp	$6171$	$2$	6171.a	1.a	$1$	$20$	$20$	$49.276$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$1$	$0$	$-3$	$-20$	$7$	$5$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{12}q^{5}+\cdots$
6171.2.a.bq	$6171$	$2$	6171.a	1.a	$1$	$20$	$20$	$49.276$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$1$	$0$	$-1$	$20$	$17$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{13}+\cdots)q^{5}+\cdots$
6171.2.a.br	$6171$	$2$	6171.a	1.a	$1$	$20$	$20$	$49.276$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$1$	$0$	$1$	$20$	$17$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{13}+\cdots)q^{5}+\cdots$
6171.2.a.bs	$6171$	$2$	6171.a	1.a	$1$	$20$	$20$	$49.276$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$1$	$0$	$3$	$-20$	$7$	$-5$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{12}q^{5}+\cdots$

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Elliptic curves over $\Q$
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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.