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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 (23 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	13	103	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2678.2.a.a	$2678$	$2$	2678.a	1.a	$1$	$1$	$1$	$21.384$	$\Q$	None	✓	$1$	$2$	$-1$	$-2$	$-2$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}-2q^{5}+2q^{6}-q^{7}+\cdots$
2678.2.a.b	$2678$	$2$	2678.a	1.a	$1$	$1$	$1$	$21.384$	$\Q$	None	✓	$1$	$1$	$-1$	$-2$	$0$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{7}-q^{8}+\cdots$
2678.2.a.c	$2678$	$2$	2678.a	1.a	$1$	$1$	$1$	$21.384$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$-3$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-3q^{7}+\cdots$
2678.2.a.d	$2678$	$2$	2678.a	1.a	$1$	$1$	$1$	$21.384$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$3$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-q^{8}+\cdots$
2678.2.a.e	$2678$	$2$	2678.a	1.a	$1$	$1$	$1$	$21.384$	$\Q$	None	✓	$1$	$0$	$-1$	$2$	$-2$	$3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{5}-2q^{6}+3q^{7}+\cdots$
2678.2.a.f	$2678$	$2$	2678.a	1.a	$1$	$1$	$1$	$21.384$	$\Q$	None	✓	$1$	$1$	$-1$	$2$	$0$	$-5$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-5q^{7}-q^{8}+\cdots$
2678.2.a.g	$2678$	$2$	2678.a	1.a	$1$	$1$	$1$	$21.384$	$\Q$	None	✓	$1$	$1$	$-1$	$2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots$
2678.2.a.h	$2678$	$2$	2678.a	1.a	$1$	$1$	$1$	$21.384$	$\Q$	None	✓	$1$	$0$	$-1$	$3$	$1$	$5$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}+q^{5}-3q^{6}+5q^{7}+\cdots$
2678.2.a.i	$2678$	$2$	2678.a	1.a	$1$	$1$	$1$	$21.384$	$\Q$	None	✓	$1$	$2$	$1$	$-2$	$-4$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-4q^{5}-2q^{6}-3q^{7}+\cdots$
2678.2.a.j	$2678$	$2$	2678.a	1.a	$1$	$1$	$1$	$21.384$	$\Q$	None	✓	$1$	$1$	$1$	$-2$	$2$	$-3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}+2q^{5}-2q^{6}-3q^{7}+\cdots$
2678.2.a.k	$2678$	$2$	2678.a	1.a	$1$	$1$	$1$	$21.384$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-2$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-3q^{9}+\cdots$
2678.2.a.l	$2678$	$2$	2678.a	1.a	$1$	$1$	$1$	$21.384$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
2678.2.a.m	$2678$	$2$	2678.a	1.a	$1$	$1$	$1$	$21.384$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$1$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-4q^{7}+\cdots$
2678.2.a.n	$2678$	$2$	2678.a	1.a	$1$	$1$	$1$	$21.384$	$\Q$	None	✓	$1$	$0$	$1$	$3$	$-1$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}-q^{5}+3q^{6}+4q^{7}+\cdots$
2678.2.a.o	$2678$	$2$	2678.a	1.a	$1$	$2$	$2$	$21.384$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-3$	$-2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta )q^{3}+q^{4}-2\beta q^{5}+\cdots$
2678.2.a.p	$2678$	$2$	2678.a	1.a	$1$	$3$	$3$	$21.384$	3.3.621.1	None	✓	$1$	$1$	$-3$	$-3$	$0$	$3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots$
2678.2.a.q	$2678$	$2$	2678.a	1.a	$1$	$3$	$3$	$21.384$	3.3.316.1	None	✓	$1$	$1$	$3$	$-4$	$0$	$-5$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta _{1})q^{3}+q^{4}+\beta _{2}q^{5}+\cdots$
2678.2.a.r	$2678$	$2$	2678.a	1.a	$1$	$10$	$10$	$21.384$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$-10$	$0$	$9$	$9$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{3})q^{5}-\beta _{1}q^{6}+\cdots$
2678.2.a.s	$2678$	$2$	2678.a	1.a	$1$	$10$	$10$	$21.384$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$10$	$-6$	$-3$	$-10$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}-\beta _{5}q^{5}+\cdots$
2678.2.a.t	$2678$	$2$	2678.a	1.a	$1$	$11$	$11$	$21.384$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$11$	$6$	$7$	$7$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1+\beta _{5})q^{5}+\cdots$
2678.2.a.u	$2678$	$2$	2678.a	1.a	$1$	$14$	$14$	$21.384$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$1$	$-14$	$0$	$-5$	$-11$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots$
2678.2.a.v	$2678$	$2$	2678.a	1.a	$1$	$15$	$15$	$21.384$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$0$	$-15$	$0$	$3$	$3$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}-\beta _{1}q^{6}+\cdots$
2678.2.a.w	$2678$	$2$	2678.a	1.a	$1$	$19$	$19$	$21.384$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	None	✓	$1$	$0$	$19$	$6$	$1$	$13$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{8}q^{5}+\beta _{1}q^{6}+\cdots$

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