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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 (33 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	5	223	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6690.2.a.a	$6690$	$2$	6690.a	1.a	$1$	$1$	$1$	$53.420$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$-1$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$
6690.2.a.b	$6690$	$2$	6690.a	1.a	$1$	$1$	$1$	$53.420$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$-1$	$1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
6690.2.a.c	$6690$	$2$	6690.a	1.a	$1$	$1$	$1$	$53.420$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$1$	$3$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+3q^{7}+\cdots$
6690.2.a.d	$6690$	$2$	6690.a	1.a	$1$	$1$	$1$	$53.420$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$-1$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
6690.2.a.e	$6690$	$2$	6690.a	1.a	$1$	$1$	$1$	$53.420$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$1$	$-3$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-3q^{7}+\cdots$
6690.2.a.f	$6690$	$2$	6690.a	1.a	$1$	$1$	$1$	$53.420$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$1$	$3$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots$
6690.2.a.g	$6690$	$2$	6690.a	1.a	$1$	$1$	$1$	$53.420$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$-1$	$-4$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots$
6690.2.a.h	$6690$	$2$	6690.a	1.a	$1$	$1$	$1$	$53.420$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$-1$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
6690.2.a.i	$6690$	$2$	6690.a	1.a	$1$	$1$	$1$	$53.420$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$-1$	$-4$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-4q^{7}+\cdots$
6690.2.a.j	$6690$	$2$	6690.a	1.a	$1$	$1$	$1$	$53.420$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$1$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
6690.2.a.k	$6690$	$2$	6690.a	1.a	$1$	$1$	$1$	$53.420$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$1$	$4$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots$
6690.2.a.l	$6690$	$2$	6690.a	1.a	$1$	$2$	$2$	$53.420$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$-2$	$-2$	$-2$	$1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+\beta q^{7}+\cdots$
6690.2.a.m	$6690$	$2$	6690.a	1.a	$1$	$2$	$2$	$53.420$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-2$	$-2$	$-2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-2\beta q^{7}+\cdots$
6690.2.a.n	$6690$	$2$	6690.a	1.a	$1$	$3$	$3$	$53.420$	3.3.1509.1	None	✓	$1$	$0$	$3$	$-3$	$-3$	$4$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
6690.2.a.o	$6690$	$2$	6690.a	1.a	$1$	$4$	$4$	$53.420$	4.4.48389.1	None	✓	$1$	$0$	$-4$	$4$	$-4$	$5$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
6690.2.a.p	$6690$	$2$	6690.a	1.a	$1$	$4$	$4$	$53.420$	4.4.84677.1	None	✓	$1$	$0$	$4$	$4$	$4$	$-6$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots$
6690.2.a.q	$6690$	$2$	6690.a	1.a	$1$	$4$	$4$	$53.420$	4.4.725.1	None	✓	$1$	$1$	$4$	$4$	$4$	$-5$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots$
6690.2.a.r	$6690$	$2$	6690.a	1.a	$1$	$5$	$5$	$53.420$	5.5.81589.1	None	✓	$1$	$0$	$-5$	$-5$	$-5$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots$
6690.2.a.s	$6690$	$2$	6690.a	1.a	$1$	$5$	$5$	$53.420$	5.5.1052869.1	None	✓	$1$	$0$	$-5$	$5$	$-5$	$8$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
6690.2.a.t	$6690$	$2$	6690.a	1.a	$1$	$5$	$5$	$53.420$	5.5.8693777.1	None	✓	$1$	$0$	$-5$	$5$	$5$	$3$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
6690.2.a.u	$6690$	$2$	6690.a	1.a	$1$	$5$	$5$	$53.420$	5.5.2817605.1	None	✓	$1$	$0$	$5$	$-5$	$-5$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(-\beta _{3}+\cdots)q^{7}+\cdots$
6690.2.a.v	$6690$	$2$	6690.a	1.a	$1$	$6$	$6$	$53.420$	6.6.11623961.1	None	✓	$1$	$1$	$-6$	$6$	$6$	$-6$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
6690.2.a.w	$6690$	$2$	6690.a	1.a	$1$	$6$	$6$	$53.420$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$0$	$-6$	$6$	$6$	$3$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
6690.2.a.x	$6690$	$2$	6690.a	1.a	$1$	$6$	$6$	$53.420$	6.6.5173625.1	None	✓	$1$	$1$	$6$	$-6$	$-6$	$5$	$-$	$+$	$+$	$-$	$+$	$5$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(1-\beta _{4}+\cdots)q^{7}+\cdots$
6690.2.a.y	$6690$	$2$	6690.a	1.a	$1$	$6$	$6$	$53.420$	6.6.6848593.1	None	✓	$1$	$1$	$6$	$-6$	$6$	$-1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots$
6690.2.a.z	$6690$	$2$	6690.a	1.a	$1$	$6$	$6$	$53.420$	6.6.5224841.1	None	✓	$1$	$1$	$6$	$6$	$-6$	$-5$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
6690.2.a.ba	$6690$	$2$	6690.a	1.a	$1$	$8$	$8$	$53.420$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-8$	$-8$	$8$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-\beta _{6}q^{7}+\cdots$
6690.2.a.bb	$6690$	$2$	6690.a	1.a	$1$	$8$	$8$	$53.420$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-8$	$8$	$-8$	$-8$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
6690.2.a.bc	$6690$	$2$	6690.a	1.a	$1$	$9$	$9$	$53.420$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$-9$	$-9$	$9$	$-7$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
6690.2.a.bd	$6690$	$2$	6690.a	1.a	$1$	$9$	$9$	$53.420$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$9$	$9$	$9$	$8$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(1+\beta _{7}+\cdots)q^{7}+\cdots$
6690.2.a.be	$6690$	$2$	6690.a	1.a	$1$	$10$	$10$	$53.420$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-10$	$-10$	$-10$	$-2$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
6690.2.a.bf	$6690$	$2$	6690.a	1.a	$1$	$12$	$12$	$53.420$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$12$	$12$	$-12$	$11$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
6690.2.a.bg	$6690$	$2$	6690.a	1.a	$1$	$13$	$13$	$53.420$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$13$	$-13$	$13$	$3$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+\beta _{1}q^{7}+\cdots$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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.