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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 (49 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	13	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9633.2.a.a	$9633$	$2$	9633.a	1.a	$1$	$1$	$1$	$76.920$	$\Q$	None	✓	$1$	$0$	$-2$	$-1$	$-2$	$3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}-2q^{5}+2q^{6}+\cdots$
9633.2.a.b	$9633$	$2$	9633.a	1.a	$1$	$1$	$1$	$76.920$	$\Q$	None	✓	$1$	$1$	$-2$	$1$	$-4$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-4q^{5}-2q^{6}+\cdots$
9633.2.a.c	$9633$	$2$	9633.a	1.a	$1$	$1$	$1$	$76.920$	$\Q$	None	✓	$1$	$1$	$-2$	$1$	$-1$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}+q^{7}+\cdots$
9633.2.a.d	$9633$	$2$	9633.a	1.a	$1$	$1$	$1$	$76.920$	$\Q$	None	✓	$1$	$0$	$-2$	$1$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-2q^{6}-q^{7}+q^{9}+\cdots$
9633.2.a.e	$9633$	$2$	9633.a	1.a	$1$	$1$	$1$	$76.920$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$-1$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}-3q^{7}+\cdots$
9633.2.a.f	$9633$	$2$	9633.a	1.a	$1$	$1$	$1$	$76.920$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$3$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+3q^{5}+q^{6}-q^{7}+\cdots$
9633.2.a.g	$9633$	$2$	9633.a	1.a	$1$	$1$	$1$	$76.920$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$-3$	$-5$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-3q^{5}-q^{6}-5q^{7}+\cdots$
9633.2.a.h	$9633$	$2$	9633.a	1.a	$1$	$1$	$1$	$76.920$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+2q^{5}-q^{6}+3q^{8}+\cdots$
9633.2.a.i	$9633$	$2$	9633.a	1.a	$1$	$1$	$1$	$76.920$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-2$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-2q^{5}+3q^{7}+q^{9}-6q^{11}+\cdots$
9633.2.a.j	$9633$	$2$	9633.a	1.a	$1$	$1$	$1$	$76.920$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-1$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}+3q^{7}+q^{9}+3q^{11}+\cdots$
9633.2.a.k	$9633$	$2$	9633.a	1.a	$1$	$1$	$1$	$76.920$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-3q^{7}+q^{9}-2q^{11}+\cdots$
9633.2.a.l	$9633$	$2$	9633.a	1.a	$1$	$1$	$1$	$76.920$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+3q^{7}+q^{9}+2q^{11}+\cdots$
9633.2.a.m	$9633$	$2$	9633.a	1.a	$1$	$1$	$1$	$76.920$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$2$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+2q^{5}-3q^{7}+q^{9}+6q^{11}+\cdots$
9633.2.a.n	$9633$	$2$	9633.a	1.a	$1$	$1$	$1$	$76.920$	$\Q$	None	✓	$1$	$1$	$2$	$-1$	$2$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}+2q^{5}-2q^{6}+\cdots$
9633.2.a.o	$9633$	$2$	9633.a	1.a	$1$	$1$	$1$	$76.920$	$\Q$	None	✓	$1$	$0$	$2$	$-1$	$3$	$5$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}+3q^{5}-2q^{6}+\cdots$
9633.2.a.p	$9633$	$2$	9633.a	1.a	$1$	$1$	$1$	$76.920$	$\Q$	None	✓	$1$	$1$	$2$	$1$	$-1$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-3q^{7}+\cdots$
9633.2.a.q	$9633$	$2$	9633.a	1.a	$1$	$1$	$1$	$76.920$	$\Q$	None	✓	$1$	$1$	$2$	$1$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+2q^{6}+q^{7}+q^{9}+\cdots$
9633.2.a.r	$9633$	$2$	9633.a	1.a	$1$	$1$	$1$	$76.920$	$\Q$	None	✓	$1$	$0$	$2$	$1$	$4$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+4q^{5}+2q^{6}+\cdots$
9633.2.a.s	$9633$	$2$	9633.a	1.a	$1$	$2$	$2$	$76.920$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$-1$	$-2$	$-2$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(2+\beta )q^{4}-q^{5}+\beta q^{6}+\cdots$
9633.2.a.t	$9633$	$2$	9633.a	1.a	$1$	$2$	$2$	$76.920$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$2$	$2$	$6$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+q^{5}+\beta q^{6}+(3-\beta )q^{7}+\cdots$
9633.2.a.u	$9633$	$2$	9633.a	1.a	$1$	$3$	$3$	$76.920$	3.3.621.1	None	✓	$1$	$1$	$0$	$3$	$3$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
9633.2.a.v	$9633$	$2$	9633.a	1.a	$1$	$4$	$4$	$76.920$	4.4.11324.1	None	✓	$1$	$1$	$1$	$-4$	$4$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots$
9633.2.a.w	$9633$	$2$	9633.a	1.a	$1$	$5$	$5$	$76.920$	5.5.2762272.1	None	✓	$1$	$1$	$-1$	$-5$	$-3$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots$
9633.2.a.x	$9633$	$2$	9633.a	1.a	$1$	$5$	$5$	$76.920$	5.5.504568.1	None	✓	$1$	$0$	$1$	$-5$	$1$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{2}+\beta _{4})q^{5}+\cdots$
9633.2.a.y	$9633$	$2$	9633.a	1.a	$1$	$6$	$6$	$76.920$	6.6.181100529.1	None	✓	$1$	$1$	$-1$	$6$	$-4$	$-6$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
9633.2.a.z	$9633$	$2$	9633.a	1.a	$1$	$6$	$6$	$76.920$	6.6.181100529.1	None	✓	$1$	$0$	$1$	$6$	$4$	$6$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
9633.2.a.ba	$9633$	$2$	9633.a	1.a	$1$	$9$	$9$	$76.920$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$-3$	$-9$	$-8$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{6}-\beta _{7})q^{4}+(\beta _{4}+\cdots)q^{5}+\cdots$
9633.2.a.bb	$9633$	$2$	9633.a	1.a	$1$	$9$	$9$	$76.920$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$0$	$9$	$0$	$-4$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots$
9633.2.a.bc	$9633$	$2$	9633.a	1.a	$1$	$9$	$9$	$76.920$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$3$	$-9$	$8$	$3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{6}-\beta _{7})q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots$
9633.2.a.bd	$9633$	$2$	9633.a	1.a	$1$	$10$	$10$	$76.920$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-3$	$-10$	$-2$	$-6$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{9}q^{5}+\cdots$
9633.2.a.be	$9633$	$2$	9633.a	1.a	$1$	$10$	$10$	$76.920$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-3$	$10$	$-2$	$-10$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{9}q^{5}+\cdots$
9633.2.a.bf	$9633$	$2$	9633.a	1.a	$1$	$10$	$10$	$76.920$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$3$	$-10$	$2$	$6$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{9}q^{5}+\cdots$
9633.2.a.bg	$9633$	$2$	9633.a	1.a	$1$	$10$	$10$	$76.920$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$3$	$10$	$2$	$10$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+\beta _{9}q^{5}+\cdots$
9633.2.a.bh	$9633$	$2$	9633.a	1.a	$1$	$11$	$11$	$76.920$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$1$	$-2$	$-11$	$-4$	$-6$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots$
9633.2.a.bi	$9633$	$2$	9633.a	1.a	$1$	$11$	$11$	$76.920$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$1$	$-2$	$11$	$-4$	$-10$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots$
9633.2.a.bj	$9633$	$2$	9633.a	1.a	$1$	$11$	$11$	$76.920$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$2$	$-11$	$4$	$6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots$
9633.2.a.bk	$9633$	$2$	9633.a	1.a	$1$	$11$	$11$	$76.920$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$2$	$11$	$4$	$10$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots$
9633.2.a.bl	$9633$	$2$	9633.a	1.a	$1$	$18$	$18$	$76.920$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$1$	$-2$	$18$	$1$	$-5$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+\beta _{16}q^{5}-\beta _{1}q^{6}+\cdots$
9633.2.a.bm	$9633$	$2$	9633.a	1.a	$1$	$18$	$18$	$76.920$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$1$	$2$	$18$	$-1$	$5$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-\beta _{16}q^{5}+\beta _{1}q^{6}+\cdots$
9633.2.a.bn	$9633$	$2$	9633.a	1.a	$1$	$22$	$22$	$76.920$		None	✓	$1$	$1$	$-4$	$-22$	$-8$	$-12$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
9633.2.a.bo	$9633$	$2$	9633.a	1.a	$1$	$22$	$22$	$76.920$		None	✓	$1$	$1$	$-4$	$22$	$-8$	$-20$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
9633.2.a.bp	$9633$	$2$	9633.a	1.a	$1$	$22$	$22$	$76.920$		None	✓	$1$	$0$	$4$	$-22$	$8$	$12$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
9633.2.a.bq	$9633$	$2$	9633.a	1.a	$1$	$22$	$22$	$76.920$		None	✓	$1$	$0$	$4$	$22$	$8$	$20$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
9633.2.a.br	$9633$	$2$	9633.a	1.a	$1$	$24$	$24$	$76.920$		None	✓	$1$	$0$	$-4$	$-24$	$1$	$5$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
9633.2.a.bs	$9633$	$2$	9633.a	1.a	$1$	$24$	$24$	$76.920$		None	✓	$1$	$0$	$4$	$-24$	$-1$	$-5$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
9633.2.a.bt	$9633$	$2$	9633.a	1.a	$1$	$30$	$30$	$76.920$		None	✓	$1$	$1$	$-4$	$-30$	$0$	$4$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
9633.2.a.bu	$9633$	$2$	9633.a	1.a	$1$	$30$	$30$	$76.920$		None	✓	$1$	$1$	$4$	$-30$	$0$	$-4$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
9633.2.a.bv	$9633$	$2$	9633.a	1.a	$1$	$36$	$36$	$76.920$		None	✓	$1$	$0$	$-2$	$36$	$2$	$-4$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
9633.2.a.bw	$9633$	$2$	9633.a	1.a	$1$	$36$	$36$	$76.920$		None	✓	$1$	$0$	$2$	$36$	$-2$	$4$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

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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.