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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 (30 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	13	103	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8034.2.a.a	$8034$	$2$	8034.a	1.a	$1$	$1$	$1$	$64.152$	$\Q$	None	✓	$1$	$2$	$-1$	$-1$	$-4$	$1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}+q^{7}+\cdots$
8034.2.a.b	$8034$	$2$	8034.a	1.a	$1$	$1$	$1$	$64.152$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$0$	$-3$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-3q^{7}-q^{8}+\cdots$
8034.2.a.c	$8034$	$2$	8034.a	1.a	$1$	$1$	$1$	$64.152$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$1$	$3$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots$
8034.2.a.d	$8034$	$2$	8034.a	1.a	$1$	$1$	$1$	$64.152$	$\Q$	None	✓	$1$	$2$	$1$	$-1$	$-2$	$-5$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-5q^{7}+\cdots$
8034.2.a.e	$8034$	$2$	8034.a	1.a	$1$	$1$	$1$	$64.152$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$-2$	$4$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+4q^{7}+\cdots$
8034.2.a.f	$8034$	$2$	8034.a	1.a	$1$	$1$	$1$	$64.152$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$4$	$-5$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}-5q^{7}+\cdots$
8034.2.a.g	$8034$	$2$	8034.a	1.a	$1$	$1$	$1$	$64.152$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$-2$	$-4$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-4q^{7}+\cdots$
8034.2.a.h	$8034$	$2$	8034.a	1.a	$1$	$1$	$1$	$64.152$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$0$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots$
8034.2.a.i	$8034$	$2$	8034.a	1.a	$1$	$1$	$1$	$64.152$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
8034.2.a.j	$8034$	$2$	8034.a	1.a	$1$	$1$	$1$	$64.152$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$2$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{8}+\cdots$
8034.2.a.k	$8034$	$2$	8034.a	1.a	$1$	$1$	$1$	$64.152$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$4$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}-q^{7}+\cdots$
8034.2.a.l	$8034$	$2$	8034.a	1.a	$1$	$2$	$2$	$64.152$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$-2$	$-2$	$-4$	$3$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+(1+\beta )q^{7}+\cdots$
8034.2.a.m	$8034$	$2$	8034.a	1.a	$1$	$2$	$2$	$64.152$	$\Q(\sqrt{65}) $	None	✓	$1$	$1$	$-2$	$-2$	$0$	$2$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots$
8034.2.a.n	$8034$	$2$	8034.a	1.a	$1$	$4$	$4$	$64.152$	4.4.72329.1	None	✓	$1$	$0$	$4$	$4$	$2$	$5$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1+\beta _{2})q^{5}+q^{6}+\cdots$
8034.2.a.o	$8034$	$2$	8034.a	1.a	$1$	$7$	$7$	$64.152$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$-7$	$-7$	$2$	$-9$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots$
8034.2.a.p	$8034$	$2$	8034.a	1.a	$1$	$8$	$8$	$64.152$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$8$	$8$	$-8$	$-6$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1+\beta _{5}+\beta _{7})q^{5}+\cdots$
8034.2.a.q	$8034$	$2$	8034.a	1.a	$1$	$8$	$8$	$64.152$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$8$	$8$	$-6$	$-3$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots$
8034.2.a.r	$8034$	$2$	8034.a	1.a	$1$	$9$	$9$	$64.152$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$9$	$-9$	$-4$	$-4$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}-\beta _{3}q^{7}+\cdots$
8034.2.a.s	$8034$	$2$	8034.a	1.a	$1$	$10$	$10$	$64.152$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-10$	$-10$	$6$	$-9$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1+\beta _{8})q^{5}+q^{6}+\cdots$
8034.2.a.t	$8034$	$2$	8034.a	1.a	$1$	$11$	$11$	$64.152$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$-11$	$11$	$4$	$4$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-\beta _{8}q^{7}+\cdots$
8034.2.a.u	$8034$	$2$	8034.a	1.a	$1$	$11$	$11$	$64.152$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$1$	$11$	$-11$	$-2$	$-2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta _{9}q^{5}-q^{6}-\beta _{10}q^{7}+\cdots$
8034.2.a.v	$8034$	$2$	8034.a	1.a	$1$	$11$	$11$	$64.152$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$11$	$11$	$5$	$4$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}-\beta _{9}q^{7}+\cdots$
8034.2.a.w	$8034$	$2$	8034.a	1.a	$1$	$12$	$12$	$64.152$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$-12$	$12$	$-4$	$0$	$+$	$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+\beta _{11}q^{5}-q^{6}-\beta _{9}q^{7}+\cdots$
8034.2.a.x	$8034$	$2$	8034.a	1.a	$1$	$13$	$13$	$64.152$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$-13$	$13$	$1$	$-1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+\beta _{3}q^{7}+\cdots$
8034.2.a.y	$8034$	$2$	8034.a	1.a	$1$	$13$	$13$	$64.152$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$13$	$-13$	$3$	$5$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta _{8}q^{5}-q^{6}+\beta _{1}q^{7}+\cdots$
8034.2.a.z	$8034$	$2$	8034.a	1.a	$1$	$14$	$14$	$64.152$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$-14$	$-14$	$-3$	$4$	$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+\beta _{6}q^{7}+\cdots$
8034.2.a.ba	$8034$	$2$	8034.a	1.a	$1$	$14$	$14$	$64.152$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$-14$	$-14$	$-1$	$5$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}-\beta _{7}q^{7}+\cdots$
8034.2.a.bb	$8034$	$2$	8034.a	1.a	$1$	$14$	$14$	$64.152$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$1$	$-14$	$14$	$-6$	$-4$	$+$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}+\beta _{6}q^{7}+\cdots$
8034.2.a.bc	$8034$	$2$	8034.a	1.a	$1$	$15$	$15$	$64.152$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$0$	$15$	$-15$	$-1$	$5$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}-\beta _{12}q^{7}+\cdots$
8034.2.a.bd	$8034$	$2$	8034.a	1.a	$1$	$16$	$16$	$64.152$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$0$	$16$	$16$	$5$	$4$	$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}-\beta _{9}q^{7}+\cdots$

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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.