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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 (20 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	3	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2166.4.a.b	$2166$	$4$	2166.a	1.a	$1$	$1$	$1$	$127.798$	$\Q$	None	✓	$1$	$1$	$-2$	$3$	$-6$	$19$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}-6q^{5}-6q^{6}+\cdots$
2166.4.a.c	$2166$	$4$	2166.a	1.a	$1$	$1$	$1$	$127.798$	$\Q$	None	✓	$1$	$1$	$-2$	$3$	$2$	$-21$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}+2q^{5}-6q^{6}+\cdots$
2166.4.a.h	$2166$	$4$	2166.a	1.a	$1$	$1$	$1$	$127.798$	$\Q$	None	✓	$1$	$1$	$2$	$3$	$-19$	$9$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}-19q^{5}+6q^{6}+\cdots$
2166.4.a.i	$2166$	$4$	2166.a	1.a	$1$	$1$	$1$	$127.798$	$\Q$	None	✓	$1$	$1$	$2$	$3$	$6$	$-16$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+6q^{5}+6q^{6}+\cdots$
2166.4.a.j	$2166$	$4$	2166.a	1.a	$1$	$2$	$2$	$127.798$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-4$	$-6$	$-13$	$-17$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+(-4-5\beta )q^{5}+\cdots$
2166.4.a.k	$2166$	$4$	2166.a	1.a	$1$	$2$	$2$	$127.798$	$\Q(\sqrt{30}) $	None	✓	$1$	$1$	$-4$	$-6$	$8$	$18$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+(4+\beta )q^{5}+6q^{6}+\cdots$
2166.4.a.l	$2166$	$4$	2166.a	1.a	$1$	$2$	$2$	$127.798$	$\Q(\sqrt{273}) $	None	✓	$1$	$1$	$-4$	$-6$	$11$	$9$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+(6-\beta )q^{5}+6q^{6}+\cdots$
2166.4.a.m	$2166$	$4$	2166.a	1.a	$1$	$2$	$2$	$127.798$	$\Q(\sqrt{313}) $	None	✓	$1$	$1$	$-4$	$6$	$-15$	$9$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}+(-7-\beta )q^{5}+\cdots$
2166.4.a.o	$2166$	$4$	2166.a	1.a	$1$	$2$	$2$	$127.798$	$\Q(\sqrt{313}) $	None	✓	$1$	$1$	$4$	$-6$	$-15$	$9$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}+(-7-\beta )q^{5}+\cdots$
2166.4.a.p	$2166$	$4$	2166.a	1.a	$1$	$2$	$2$	$127.798$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$4$	$6$	$-13$	$-17$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+(-4-5\beta )q^{5}+\cdots$
2166.4.a.u	$2166$	$4$	2166.a	1.a	$1$	$3$	$3$	$127.798$	3.3.14457.1	None	✓	$1$	$1$	$6$	$-9$	$10$	$7$	$-$	$+$	$+$	$-$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}+(3-\beta _{1})q^{5}+\cdots$
2166.4.a.w	$2166$	$4$	2166.a	1.a	$1$	$3$	$3$	$127.798$	3.3.1524.1	None	✓	$1$	$1$	$6$	$9$	$2$	$-17$	$-$	$-$	$-$	$-$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+(1-\beta _{2})q^{5}+\cdots$
2166.4.a.x	$2166$	$4$	2166.a	1.a	$1$	$4$	$4$	$127.798$	4.4.184225.1	None	✓	$1$	$1$	$-8$	$-12$	$-28$	$-17$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+(-7+2\beta _{2}+\cdots)q^{5}+\cdots$
2166.4.a.ba	$2166$	$4$	2166.a	1.a	$1$	$4$	$4$	$127.798$	4.4.184225.1	None	✓	$1$	$1$	$8$	$12$	$-28$	$-17$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+(-7+2\beta _{2}+\cdots)q^{5}+\cdots$
2166.4.a.bf	$2166$	$4$	2166.a	1.a	$1$	$6$	$6$	$127.798$	6.6.$\cdots$.1	None	✓	$1$	$1$	$12$	$-18$	$27$	$-42$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}+(4+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
2166.4.a.bg	$2166$	$4$	2166.a	1.a	$1$	$6$	$6$	$127.798$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$1$	$12$	$18$	$-3$	$-12$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+(-1+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots$
2166.4.a.bh	$2166$	$4$	2166.a	1.a	$1$	$8$	$8$	$127.798$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-16$	$24$	$-30$	$-34$	$+$	$-$	$+$	$-$	$19$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}+(-4-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$
2166.4.a.bi	$2166$	$4$	2166.a	1.a	$1$	$8$	$8$	$127.798$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$16$	$-24$	$-30$	$-34$	$-$	$+$	$+$	$-$	$19$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}+(-4-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$
2166.4.a.bj	$2166$	$4$	2166.a	1.a	$1$	$9$	$9$	$127.798$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$-18$	$-27$	$27$	$0$	$+$	$+$	$-$	$-$	$3\cdot 19$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+(3+\beta _{1})q^{5}+\cdots$
2166.4.a.bk	$2166$	$4$	2166.a	1.a	$1$	$9$	$9$	$127.798$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$-18$	$27$	$-3$	$30$	$+$	$-$	$+$	$-$	$19$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}+\beta _{1}q^{5}-6q^{6}+\cdots$

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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.