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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 (42 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	7	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6776.2.a.a	$6776$	$2$	6776.a	1.a	$1$	$1$	$1$	$54.107$	$\Q$	None	✓	$1$	$0$	$0$	$-3$	$-3$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-3q^{5}-q^{7}+6q^{9}+4q^{13}+\cdots$
6776.2.a.b	$6776$	$2$	6776.a	1.a	$1$	$1$	$1$	$54.107$	$\Q$	None	✓	$1$	$2$	$0$	$-3$	$-3$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-3q^{5}+q^{7}+6q^{9}-4q^{13}+\cdots$
6776.2.a.c	$6776$	$2$	6776.a	1.a	$1$	$1$	$1$	$54.107$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$2$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}-q^{7}+q^{9}-4q^{13}+\cdots$
6776.2.a.d	$6776$	$2$	6776.a	1.a	$1$	$1$	$1$	$54.107$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-1$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}-2q^{9}+q^{15}+2q^{17}+\cdots$
6776.2.a.e	$6776$	$2$	6776.a	1.a	$1$	$1$	$1$	$54.107$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-2$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}-3q^{9}-2q^{13}+2q^{17}+\cdots$
6776.2.a.f	$6776$	$2$	6776.a	1.a	$1$	$1$	$1$	$54.107$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-3q^{9}+6q^{13}+2q^{19}+4q^{23}+\cdots$
6776.2.a.g	$6776$	$2$	6776.a	1.a	$1$	$1$	$1$	$54.107$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$2$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}-3q^{9}-2q^{13}+6q^{17}+\cdots$
6776.2.a.h	$6776$	$2$	6776.a	1.a	$1$	$1$	$1$	$54.107$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$-4$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-4q^{5}-q^{7}+q^{9}-8q^{15}+\cdots$
6776.2.a.i	$6776$	$2$	6776.a	1.a	$1$	$1$	$1$	$54.107$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$2$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{5}-q^{7}+q^{9}+4q^{15}+\cdots$
6776.2.a.j	$6776$	$2$	6776.a	1.a	$1$	$2$	$2$	$54.107$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-2$	$-2$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2\beta q^{3}-2\beta q^{5}-q^{7}+(1+4\beta )q^{9}+\cdots$
6776.2.a.k	$6776$	$2$	6776.a	1.a	$1$	$2$	$2$	$54.107$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$-2$	$-2$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2\beta q^{3}-2\beta q^{5}+q^{7}+(1+4\beta )q^{9}+\cdots$
6776.2.a.l	$6776$	$2$	6776.a	1.a	$1$	$2$	$2$	$54.107$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$-1$	$-3$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-2+\beta )q^{5}+q^{7}+(1+\beta )q^{9}+\cdots$
6776.2.a.m	$6776$	$2$	6776.a	1.a	$1$	$2$	$2$	$54.107$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-1$	$0$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1-2\beta )q^{5}-q^{7}+(-2+\beta )q^{9}+\cdots$
6776.2.a.n	$6776$	$2$	6776.a	1.a	$1$	$2$	$2$	$54.107$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-1$	$0$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1-2\beta )q^{5}+q^{7}+(-2+\beta )q^{9}+\cdots$
6776.2.a.o	$6776$	$2$	6776.a	1.a	$1$	$2$	$2$	$54.107$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-2\beta q^{5}-q^{7}+(1+2\beta )q^{9}+\cdots$
6776.2.a.p	$6776$	$2$	6776.a	1.a	$1$	$2$	$2$	$54.107$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-2\beta q^{5}+q^{7}+(1+2\beta )q^{9}+\cdots$
6776.2.a.q	$6776$	$2$	6776.a	1.a	$1$	$2$	$2$	$54.107$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$2$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(1+\beta )q^{5}-q^{7}+(1+2\beta )q^{9}+\cdots$
6776.2.a.r	$6776$	$2$	6776.a	1.a	$1$	$2$	$2$	$54.107$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$2$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(1+\beta )q^{5}+q^{7}+(1+2\beta )q^{9}+\cdots$
6776.2.a.s	$6776$	$2$	6776.a	1.a	$1$	$2$	$2$	$54.107$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$6$	$-1$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+(-1+\beta )q^{5}-q^{7}+6q^{9}+\cdots$
6776.2.a.t	$6776$	$2$	6776.a	1.a	$1$	$2$	$2$	$54.107$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$6$	$-1$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-\beta q^{5}+q^{7}+6q^{9}+(5-2\beta )q^{13}+\cdots$
6776.2.a.u	$6776$	$2$	6776.a	1.a	$1$	$3$	$3$	$54.107$	3.3.316.1	None	✓	$1$	$1$	$0$	$-1$	$-3$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1+\beta _{2})q^{5}-q^{7}+\beta _{2}q^{9}+\cdots$
6776.2.a.v	$6776$	$2$	6776.a	1.a	$1$	$3$	$3$	$54.107$	3.3.1509.1	None	✓	$1$	$1$	$0$	$-1$	$-3$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}-q^{7}+(2+\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{13}+\cdots$
6776.2.a.w	$6776$	$2$	6776.a	1.a	$1$	$3$	$3$	$54.107$	3.3.316.1	None	✓	$1$	$1$	$0$	$-1$	$-3$	$3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+q^{7}+\beta _{2}q^{9}+\cdots$
6776.2.a.x	$6776$	$2$	6776.a	1.a	$1$	$3$	$3$	$54.107$	3.3.1509.1	None	✓	$1$	$1$	$0$	$-1$	$-3$	$3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+q^{7}+(2+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{13}+\cdots$
6776.2.a.y	$6776$	$2$	6776.a	1.a	$1$	$3$	$3$	$54.107$	3.3.229.1	None	✓	$1$	$0$	$0$	$1$	$1$	$-3$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}-\beta _{2}q^{5}-q^{7}+(1-\beta _{1})q^{9}+\cdots$
6776.2.a.z	$6776$	$2$	6776.a	1.a	$1$	$4$	$4$	$54.107$	4.4.31288.1	None	✓	$1$	$0$	$0$	$1$	$2$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1+\beta _{3})q^{5}-q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
6776.2.a.ba	$6776$	$2$	6776.a	1.a	$1$	$4$	$4$	$54.107$	4.4.31288.1	None	✓	$1$	$0$	$0$	$1$	$2$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1+\beta _{3})q^{5}+q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
6776.2.a.bb	$6776$	$2$	6776.a	1.a	$1$	$4$	$4$	$54.107$	4.4.11348.1	None	✓	$1$	$0$	$0$	$1$	$5$	$4$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(1-\beta _{1})q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
6776.2.a.bc	$6776$	$2$	6776.a	1.a	$1$	$5$	$5$	$54.107$	5.5.3769928.1	None	✓	$1$	$0$	$0$	$1$	$-1$	$-5$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{3}q^{5}-q^{7}+(1+\beta _{2})q^{9}+\cdots$
6776.2.a.bd	$6776$	$2$	6776.a	1.a	$1$	$5$	$5$	$54.107$	5.5.3769928.1	None	✓	$1$	$0$	$0$	$1$	$-1$	$5$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{3}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots$
6776.2.a.be	$6776$	$2$	6776.a	1.a	$1$	$6$	$6$	$54.107$	6.6.988075625.1	None	✓	$1$	$1$	$0$	$-3$	$-2$	$-6$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}-\beta _{1}q^{5}-q^{7}+(-2+\beta _{2}+\cdots)q^{9}+\cdots$
6776.2.a.bf	$6776$	$2$	6776.a	1.a	$1$	$6$	$6$	$54.107$	6.6.988075625.1	None	✓	$1$	$0$	$0$	$-3$	$-2$	$6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}-\beta _{1}q^{5}+q^{7}+(-2+\beta _{2}+\cdots)q^{9}+\cdots$
6776.2.a.bg	$6776$	$2$	6776.a	1.a	$1$	$6$	$6$	$54.107$	6.6.51592896.1	None	✓	$1$	$1$	$0$	$-2$	$0$	$-6$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{5}q^{5}-q^{7}+(-\beta _{3}+\beta _{4}+\cdots)q^{9}+\cdots$
6776.2.a.bh	$6776$	$2$	6776.a	1.a	$1$	$6$	$6$	$54.107$	6.6.51592896.1	None	✓	$1$	$1$	$0$	$-2$	$0$	$6$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{5}q^{5}+q^{7}+(-\beta _{3}+\beta _{4}+\cdots)q^{9}+\cdots$
6776.2.a.bi	$6776$	$2$	6776.a	1.a	$1$	$8$	$8$	$54.107$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$0$	$-2$	$7$	$-8$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1-\beta _{2})q^{5}-q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots$
6776.2.a.bj	$6776$	$2$	6776.a	1.a	$1$	$8$	$8$	$54.107$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$0$	$-2$	$7$	$8$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1-\beta _{2})q^{5}+q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots$
6776.2.a.bk	$6776$	$2$	6776.a	1.a	$1$	$8$	$8$	$54.107$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$0$	$2$	$-7$	$-8$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{6}q^{3}+(-1+\beta _{2})q^{5}-q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots$
6776.2.a.bl	$6776$	$2$	6776.a	1.a	$1$	$8$	$8$	$54.107$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$0$	$2$	$-7$	$8$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{6}q^{3}+(-1+\beta _{2})q^{5}+q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots$
6776.2.a.bm	$6776$	$2$	6776.a	1.a	$1$	$10$	$10$	$54.107$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$0$	$-3$	$5$	$-10$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1+\beta _{6})q^{5}-q^{7}+(2+\beta _{3}+\cdots)q^{9}+\cdots$
6776.2.a.bn	$6776$	$2$	6776.a	1.a	$1$	$10$	$10$	$54.107$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$0$	$-3$	$5$	$10$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1+\beta _{6})q^{5}+q^{7}+(2+\beta _{3}+\cdots)q^{9}+\cdots$
6776.2.a.bo	$6776$	$2$	6776.a	1.a	$1$	$10$	$10$	$54.107$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$0$	$2$	$4$	$-10$	$-$	$+$	$+$	$-$	$3$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{6}q^{5}-q^{7}+(2-\beta _{6}+\beta _{7}+\cdots)q^{9}+\cdots$
6776.2.a.bp	$6776$	$2$	6776.a	1.a	$1$	$10$	$10$	$54.107$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$0$	$2$	$4$	$10$	$+$	$-$	$+$	$-$	$3$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{6}q^{5}+q^{7}+(2-\beta _{6}+\beta _{7}+\cdots)q^{9}+\cdots$

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