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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 (38 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	7	47	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6909.2.a.a	$6909$	$2$	6909.a	1.a	$1$	$1$	$1$	$55.169$	$\Q$	None	✓	$1$	$0$	$-2$	$-1$	$3$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+3q^{5}+2q^{6}+\cdots$
6909.2.a.b	$6909$	$2$	6909.a	1.a	$1$	$1$	$1$	$55.169$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$-2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+3q^{8}+\cdots$
6909.2.a.c	$6909$	$2$	6909.a	1.a	$1$	$1$	$1$	$55.169$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+2q^{5}+q^{6}+3q^{8}+\cdots$
6909.2.a.d	$6909$	$2$	6909.a	1.a	$1$	$1$	$1$	$55.169$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$-2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}+3q^{8}+\cdots$
6909.2.a.e	$6909$	$2$	6909.a	1.a	$1$	$1$	$1$	$55.169$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}+3q^{8}+q^{9}+\cdots$
6909.2.a.f	$6909$	$2$	6909.a	1.a	$1$	$1$	$1$	$55.169$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$2$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+2q^{5}+q^{9}-2q^{11}+\cdots$
6909.2.a.g	$6909$	$2$	6909.a	1.a	$1$	$1$	$1$	$55.169$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-2q^{5}+q^{9}-2q^{11}+\cdots$
6909.2.a.h	$6909$	$2$	6909.a	1.a	$1$	$1$	$1$	$55.169$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{5}+q^{9}-3q^{11}-2q^{12}+\cdots$
6909.2.a.i	$6909$	$2$	6909.a	1.a	$1$	$1$	$1$	$55.169$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}-4q^{5}+q^{6}-3q^{8}+\cdots$
6909.2.a.j	$6909$	$2$	6909.a	1.a	$1$	$1$	$1$	$55.169$	$\Q$	None	✓	$1$	$1$	$2$	$-1$	$-4$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-4q^{5}-2q^{6}+\cdots$
6909.2.a.k	$6909$	$2$	6909.a	1.a	$1$	$1$	$1$	$55.169$	$\Q$	None	✓	$1$	$1$	$2$	$-1$	$1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+q^{9}+\cdots$
6909.2.a.l	$6909$	$2$	6909.a	1.a	$1$	$1$	$1$	$55.169$	$\Q$	None	✓	$1$	$1$	$2$	$1$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+2q^{6}+q^{9}+3q^{11}+\cdots$
6909.2.a.m	$6909$	$2$	6909.a	1.a	$1$	$2$	$2$	$55.169$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$-1$	$2$	$-1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(2+\beta )q^{4}+(-1+\beta )q^{5}+\cdots$
6909.2.a.n	$6909$	$2$	6909.a	1.a	$1$	$2$	$2$	$55.169$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$2$	$2$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+3q^{4}+(1-\beta )q^{5}-\beta q^{6}+\cdots$
6909.2.a.o	$6909$	$2$	6909.a	1.a	$1$	$3$	$3$	$55.169$	3.3.169.1	None	✓	$1$	$0$	$-1$	$-3$	$1$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
6909.2.a.p	$6909$	$2$	6909.a	1.a	$1$	$3$	$3$	$55.169$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$-1$	$3$	$1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots$
6909.2.a.q	$6909$	$2$	6909.a	1.a	$1$	$3$	$3$	$55.169$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$1$	$3$	$3$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(2-2\beta _{1}+\beta _{2})q^{5}+\cdots$
6909.2.a.r	$6909$	$2$	6909.a	1.a	$1$	$4$	$4$	$55.169$	4.4.2777.1	None	✓	$1$	$1$	$-2$	$-4$	$7$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}-q^{3}+(-\beta _{2}+\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots$
6909.2.a.s	$6909$	$2$	6909.a	1.a	$1$	$4$	$4$	$55.169$	4.4.141889.1	None	✓	$1$	$1$	$-1$	$4$	$-1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots$
6909.2.a.t	$6909$	$2$	6909.a	1.a	$1$	$5$	$5$	$55.169$	5.5.486337.1	None	✓	$1$	$1$	$0$	$-5$	$-5$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2}+\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots$
6909.2.a.u	$6909$	$2$	6909.a	1.a	$1$	$9$	$9$	$55.169$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$3$	$-9$	$-7$	$0$	$+$	$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{5}q^{2}-q^{3}+(1-\beta _{8})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
6909.2.a.v	$6909$	$2$	6909.a	1.a	$1$	$9$	$9$	$55.169$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$3$	$9$	$-3$	$0$	$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots$
6909.2.a.w	$6909$	$2$	6909.a	1.a	$1$	$10$	$10$	$55.169$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-2$	$-10$	$6$	$0$	$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{7}+\cdots)q^{5}+\cdots$
6909.2.a.x	$6909$	$2$	6909.a	1.a	$1$	$10$	$10$	$55.169$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-2$	$10$	$-6$	$0$	$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{7}+\cdots)q^{5}+\cdots$
6909.2.a.y	$6909$	$2$	6909.a	1.a	$1$	$14$	$14$	$55.169$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$2$	$-14$	$-2$	$0$	$+$	$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{9}q^{5}+\cdots$
6909.2.a.z	$6909$	$2$	6909.a	1.a	$1$	$14$	$14$	$55.169$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$2$	$14$	$2$	$0$	$-$	$-$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{9}q^{5}+\cdots$
6909.2.a.ba	$6909$	$2$	6909.a	1.a	$1$	$15$	$15$	$55.169$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$0$	$-6$	$-15$	$5$	$0$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots$
6909.2.a.bb	$6909$	$2$	6909.a	1.a	$1$	$15$	$15$	$55.169$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$1$	$-6$	$15$	$-5$	$0$	$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots$
6909.2.a.bc	$6909$	$2$	6909.a	1.a	$1$	$15$	$15$	$55.169$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$0$	$-4$	$-15$	$3$	$0$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{13}q^{5}+\cdots$
6909.2.a.bd	$6909$	$2$	6909.a	1.a	$1$	$15$	$15$	$55.169$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$1$	$-4$	$15$	$-3$	$0$	$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{13}q^{5}+\cdots$
6909.2.a.be	$6909$	$2$	6909.a	1.a	$1$	$15$	$15$	$55.169$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$1$	$2$	$-15$	$-7$	$0$	$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{8}q^{5}+\cdots$
6909.2.a.bf	$6909$	$2$	6909.a	1.a	$1$	$15$	$15$	$55.169$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$0$	$2$	$15$	$7$	$0$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots$
6909.2.a.bg	$6909$	$2$	6909.a	1.a	$1$	$16$	$16$	$55.169$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$1$	$4$	$-16$	$-7$	$0$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{9}q^{5}+\cdots$
6909.2.a.bh	$6909$	$2$	6909.a	1.a	$1$	$16$	$16$	$55.169$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$0$	$4$	$16$	$7$	$0$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{9}q^{5}+\cdots$
6909.2.a.bi	$6909$	$2$	6909.a	1.a	$1$	$18$	$18$	$55.169$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$1$	$-2$	$-18$	$8$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{13}q^{5}+\cdots$
6909.2.a.bj	$6909$	$2$	6909.a	1.a	$1$	$18$	$18$	$55.169$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$1$	$-2$	$18$	$-8$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{13}q^{5}+\cdots$
6909.2.a.bk	$6909$	$2$	6909.a	1.a	$1$	$26$	$26$	$55.169$		None	✓	$1$	$0$	$6$	$-26$	$-8$	$0$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
6909.2.a.bl	$6909$	$2$	6909.a	1.a	$1$	$26$	$26$	$55.169$		None	✓	$1$	$0$	$6$	$26$	$8$	$0$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$

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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.