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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 (29 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5780.2.a.a	$5780$	$2$	5780.a	1.a	$1$	$1$	$1$	$46.154$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}-2q^{7}+q^{9}-5q^{11}+\cdots$
5780.2.a.b	$5780$	$2$	5780.a	1.a	$1$	$1$	$1$	$46.154$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-3q^{9}-q^{11}+3q^{19}+\cdots$
5780.2.a.c	$5780$	$2$	5780.a	1.a	$1$	$1$	$1$	$46.154$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-3q^{9}+q^{11}+3q^{19}+\cdots$
5780.2.a.d	$5780$	$2$	5780.a	1.a	$1$	$1$	$1$	$46.154$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+4q^{7}-3q^{9}-2q^{11}-6q^{13}+\cdots$
5780.2.a.e	$5780$	$2$	5780.a	1.a	$1$	$1$	$1$	$46.154$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}+2q^{7}+q^{9}+5q^{11}+\cdots$
5780.2.a.f	$5780$	$2$	5780.a	1.a	$1$	$1$	$1$	$46.154$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}-2q^{7}+q^{9}+2q^{13}+\cdots$
5780.2.a.g	$5780$	$2$	5780.a	1.a	$1$	$2$	$2$	$46.154$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$-2$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-q^{5}+(-1+\beta )q^{7}+\cdots$
5780.2.a.h	$5780$	$2$	5780.a	1.a	$1$	$2$	$2$	$46.154$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}+(1+\beta )q^{7}+2\beta q^{9}+\cdots$
5780.2.a.i	$5780$	$2$	5780.a	1.a	$1$	$3$	$3$	$46.154$	3.3.1524.1	None	✓	$1$	$1$	$0$	$-2$	$3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+q^{5}+(-1-\beta _{1})q^{7}+\cdots$
5780.2.a.j	$5780$	$2$	5780.a	1.a	$1$	$3$	$3$	$46.154$	3.3.404.1	None	✓	$1$	$0$	$0$	$0$	$-3$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-q^{5}+\beta _{2}q^{7}+(2-\beta _{1}+\beta _{2})q^{9}+\cdots$
5780.2.a.k	$5780$	$2$	5780.a	1.a	$1$	$3$	$3$	$46.154$	3.3.1524.1	None	✓	$1$	$0$	$0$	$2$	$-3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}-q^{5}+(1+\beta _{1})q^{7}+(3+\cdots)q^{9}+\cdots$
5780.2.a.l	$5780$	$2$	5780.a	1.a	$1$	$6$	$6$	$46.154$	6.6.14414517.1	None	✓	$1$	$1$	$0$	$-3$	$6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{5}q^{3}+q^{5}-\beta _{2}q^{7}+\beta _{5}q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$
5780.2.a.m	$5780$	$2$	5780.a	1.a	$1$	$6$	$6$	$46.154$	6.6.9521152.1	None	✓	$1$	$0$	$0$	$0$	$-6$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{5})q^{7}+\cdots$
5780.2.a.n	$5780$	$2$	5780.a	1.a	$1$	$6$	$6$	$46.154$	6.6.9521152.1	None	✓	$1$	$1$	$0$	$0$	$6$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{5})q^{7}+\cdots$
5780.2.a.o	$5780$	$2$	5780.a	1.a	$1$	$6$	$6$	$46.154$	6.6.14414517.1	None	✓	$1$	$1$	$0$	$3$	$-6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{5}q^{3}-q^{5}+\beta _{2}q^{7}+\beta _{5}q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
5780.2.a.p	$5780$	$2$	5780.a	1.a	$1$	$12$	$12$	$46.154$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$0$	$-3$	$-12$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+\beta _{3}q^{7}+(2+\beta _{2})q^{9}+\cdots$
5780.2.a.q	$5780$	$2$	5780.a	1.a	$1$	$12$	$12$	$46.154$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$0$	$0$	$-12$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+(-1+\beta _{11})q^{7}+(1+\cdots)q^{9}+\cdots$
5780.2.a.r	$5780$	$2$	5780.a	1.a	$1$	$12$	$12$	$46.154$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$0$	$0$	$12$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+q^{5}+(1-\beta _{11})q^{7}+(1+\beta _{8}+\cdots)q^{9}+\cdots$
5780.2.a.s	$5780$	$2$	5780.a	1.a	$1$	$12$	$12$	$46.154$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$0$	$3$	$12$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}-\beta _{3}q^{7}+(2+\beta _{2})q^{9}+\cdots$
5780.2.c.a	$5780$	$2$	5780.c	17.b	$2$	$2$	$2$	$46.154$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{3}+iq^{5}+2iq^{7}-q^{9}+2q^{13}+\cdots$
5780.2.c.b	$5780$	$2$	5780.c	17.b	$2$	$2$	$2$	$46.154$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{3}-iq^{5}-2iq^{7}-q^{9}-5iq^{11}+\cdots$
5780.2.c.c	$5780$	$2$	5780.c	17.b	$2$	$2$	$2$	$46.154$	$\Q(\sqrt{-1}) $	None		$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{5}+4iq^{7}+3q^{9}-2iq^{11}-6q^{13}+\cdots$
5780.2.c.d	$5780$	$2$	5780.c	17.b	$2$	$2$	$2$	$46.154$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{5}-2iq^{7}+3q^{9}+iq^{11}-3q^{19}+\cdots$
5780.2.c.e	$5780$	$2$	5780.c	17.b	$2$	$4$	$4$	$46.154$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{8}+\zeta_{8}^{2})q^{3}+\zeta_{8}q^{5}+(-\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{7}+\cdots$
5780.2.c.f	$5780$	$2$	5780.c	17.b	$2$	$6$	$6$	$46.154$	6.0.2611456.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}-\beta _{4}q^{5}-\beta _{2}q^{7}+(-2+\beta _{1}+\cdots)q^{9}+\cdots$
5780.2.c.g	$5780$	$2$	5780.c	17.b	$2$	$12$	$12$	$46.154$	12.0.$\cdots$.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{11}q^{3}-\beta _{3}q^{5}-\beta _{6}q^{7}+\beta _{8}q^{9}+\cdots$
5780.2.c.h	$5780$	$2$	5780.c	17.b	$2$	$12$	$12$	$46.154$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{3}-\beta _{6}q^{5}+(\beta _{7}-\beta _{9}-\beta _{10}+\cdots)q^{7}+\cdots$
5780.2.c.i	$5780$	$2$	5780.c	17.b	$2$	$24$	$24$	$46.154$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
5780.2.c.j	$5780$	$2$	5780.c	17.b	$2$	$24$	$24$	$46.154$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.