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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	5	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6760.2.a.a	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$-1$	$3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}+3q^{7}+6q^{9}+5q^{11}+\cdots$
6760.2.a.b	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$1$	$-3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}-3q^{7}+6q^{9}-5q^{11}+\cdots$
6760.2.a.c	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	$\Q$	None	✓	$1$	$2$	$0$	$-1$	$-1$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-3q^{7}-2q^{9}-3q^{11}+\cdots$
6760.2.a.d	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-1$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-3q^{7}-2q^{9}+q^{11}+q^{15}+\cdots$
6760.2.a.e	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-1$	$3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+3q^{7}-2q^{9}-5q^{11}+\cdots$
6760.2.a.f	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$1$	$-3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-3q^{7}-2q^{9}+5q^{11}+\cdots$
6760.2.a.g	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$1$	$3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+3q^{7}-2q^{9}-q^{11}-q^{15}+\cdots$
6760.2.a.h	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$1$	$3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+3q^{7}-2q^{9}+3q^{11}+\cdots$
6760.2.a.i	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-1$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}-3q^{9}-4q^{11}+2q^{17}+\cdots$
6760.2.a.j	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{9}+4q^{11}-6q^{17}-4q^{19}+\cdots$
6760.2.a.k	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$-1$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}+q^{9}-2q^{11}-2q^{15}+\cdots$
6760.2.a.l	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$-1$	$3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}+3q^{7}+q^{9}-5q^{11}+\cdots$
6760.2.a.m	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$1$	$-3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}-3q^{7}+q^{9}+5q^{11}+\cdots$
6760.2.a.n	$6760$	$2$	6760.a	1.a	$1$	$2$	$2$	$53.979$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$-4$	$-2$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{3}-q^{5}+2q^{7}+(3-4\beta )q^{9}+\cdots$
6760.2.a.o	$6760$	$2$	6760.a	1.a	$1$	$2$	$2$	$53.979$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$-2$	$2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+q^{5}-2\beta q^{7}+(1-2\beta )q^{9}+\cdots$
6760.2.a.p	$6760$	$2$	6760.a	1.a	$1$	$2$	$2$	$53.979$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$-2$	$2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+q^{5}+2\beta q^{7}+(1-2\beta )q^{9}+\cdots$
6760.2.a.q	$6760$	$2$	6760.a	1.a	$1$	$2$	$2$	$53.979$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$-1$	$-2$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-q^{5}-q^{7}+(1+\beta )q^{9}+3q^{11}+\cdots$
6760.2.a.r	$6760$	$2$	6760.a	1.a	$1$	$2$	$2$	$53.979$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$-1$	$2$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+q^{5}+q^{7}+(1+\beta )q^{9}-3q^{11}+\cdots$
6760.2.a.s	$6760$	$2$	6760.a	1.a	$1$	$2$	$2$	$53.979$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$0$	$0$	$-2$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}-2q^{7}+3q^{9}+(2-\beta )q^{11}+\cdots$
6760.2.a.t	$6760$	$2$	6760.a	1.a	$1$	$2$	$2$	$53.979$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$2$	$2$	$0$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}+(3+2\beta )q^{9}+(-3+\cdots)q^{11}+\cdots$
6760.2.a.u	$6760$	$2$	6760.a	1.a	$1$	$3$	$3$	$53.979$	3.3.148.1	None	✓	$1$	$1$	$0$	$0$	$-3$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}-q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots$
6760.2.a.v	$6760$	$2$	6760.a	1.a	$1$	$3$	$3$	$53.979$	3.3.148.1	None	✓	$1$	$1$	$0$	$0$	$3$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots$
6760.2.a.w	$6760$	$2$	6760.a	1.a	$1$	$3$	$3$	$53.979$	3.3.1016.1	None	✓	$1$	$0$	$0$	$1$	$-3$	$9$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+3q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots$
6760.2.a.x	$6760$	$2$	6760.a	1.a	$1$	$3$	$3$	$53.979$	3.3.1016.1	None	✓	$1$	$0$	$0$	$1$	$3$	$-9$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}-3q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots$
6760.2.a.y	$6760$	$2$	6760.a	1.a	$1$	$3$	$3$	$53.979$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$0$	$3$	$-3$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}-\beta _{2})q^{3}-q^{5}+\beta _{2}q^{7}+(3+\cdots)q^{9}+\cdots$
6760.2.a.z	$6760$	$2$	6760.a	1.a	$1$	$3$	$3$	$53.979$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$0$	$3$	$3$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}-\beta _{2})q^{3}+q^{5}-\beta _{2}q^{7}+(3+\cdots)q^{9}+\cdots$
6760.2.a.ba	$6760$	$2$	6760.a	1.a	$1$	$4$	$4$	$53.979$	4.4.25488.1	None	✓	$1$	$0$	$0$	$0$	$-4$	$4$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}-q^{5}+(1+\beta _{1}+\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots$
6760.2.a.bb	$6760$	$2$	6760.a	1.a	$1$	$4$	$4$	$53.979$	4.4.25488.1	None	✓	$1$	$0$	$0$	$0$	$4$	$-4$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+q^{5}+(-1-\beta _{1}-\beta _{2})q^{7}+\cdots$
6760.2.a.bc	$6760$	$2$	6760.a	1.a	$1$	$4$	$4$	$53.979$	4.4.34868.1	None	✓	$1$	$0$	$0$	$2$	$-4$	$-6$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}-q^{5}+(-1-\beta _{1}-\beta _{3})q^{7}+\cdots$
6760.2.a.bd	$6760$	$2$	6760.a	1.a	$1$	$4$	$4$	$53.979$	4.4.34868.1	None	✓	$1$	$0$	$0$	$2$	$4$	$6$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+q^{5}+(1+\beta _{1}+\beta _{3})q^{7}+\cdots$
6760.2.a.be	$6760$	$2$	6760.a	1.a	$1$	$6$	$6$	$53.979$	6.6.406193977.1	None	✓	$1$	$1$	$0$	$-2$	$-6$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}-q^{5}-\beta _{1}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
6760.2.a.bf	$6760$	$2$	6760.a	1.a	$1$	$6$	$6$	$53.979$	6.6.406193977.1	None	✓	$1$	$0$	$0$	$-2$	$6$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+q^{5}+\beta _{1}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
6760.2.a.bg	$6760$	$2$	6760.a	1.a	$1$	$6$	$6$	$53.979$	6.6.7674048.1	None	✓	$1$	$1$	$0$	$0$	$-6$	$-4$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+(-\beta _{1}+\beta _{4}-\beta _{5})q^{7}+\cdots$
6760.2.a.bh	$6760$	$2$	6760.a	1.a	$1$	$6$	$6$	$53.979$	6.6.2249737.1	None	✓	$1$	$0$	$0$	$0$	$-6$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{3}-q^{5}-\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots$
6760.2.a.bi	$6760$	$2$	6760.a	1.a	$1$	$6$	$6$	$53.979$	6.6.2249737.1	None	✓	$1$	$1$	$0$	$0$	$6$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{3}+q^{5}+\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots$
6760.2.a.bj	$6760$	$2$	6760.a	1.a	$1$	$6$	$6$	$53.979$	6.6.7674048.1	None	✓	$1$	$1$	$0$	$0$	$6$	$4$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+q^{5}+(\beta _{1}-\beta _{4}+\beta _{5})q^{7}+\cdots$
6760.2.a.bk	$6760$	$2$	6760.a	1.a	$1$	$8$	$8$	$53.979$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$0$	$4$	$-8$	$-6$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+(-1+\beta _{5})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
6760.2.a.bl	$6760$	$2$	6760.a	1.a	$1$	$8$	$8$	$53.979$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$0$	$4$	$8$	$6$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+q^{5}+(1-\beta _{5})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
6760.2.a.bm	$6760$	$2$	6760.a	1.a	$1$	$9$	$9$	$53.979$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$0$	$1$	$-9$	$7$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+(1-\beta _{2}+\beta _{8})q^{7}+(1+\cdots)q^{9}+\cdots$
6760.2.a.bn	$6760$	$2$	6760.a	1.a	$1$	$9$	$9$	$53.979$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$0$	$1$	$9$	$-7$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}+(-1+\beta _{2}-\beta _{8})q^{7}+\cdots$
6760.2.a.bo	$6760$	$2$	6760.a	1.a	$1$	$12$	$12$	$53.979$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$0$	$0$	$-12$	$-7$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+(-1-\beta _{10})q^{7}+(2+\cdots)q^{9}+\cdots$
6760.2.a.bp	$6760$	$2$	6760.a	1.a	$1$	$12$	$12$	$53.979$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$0$	$0$	$12$	$7$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+q^{5}+(1+\beta _{10})q^{7}+(2+\beta _{4}+\cdots)q^{9}+\cdots$

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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.