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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (36 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	7	59	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5782.2.a.a	$5782$	$2$	5782.a	1.a	$1$	$1$	$1$	$46.170$	$\Q$	None	✓				826.2.a.b	$1$	$1$	$-1$	$-2$	$-3$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}-3q^{5}+2q^{6}-q^{8}+\cdots$
5782.2.a.b	$5782$	$2$	5782.a	1.a	$1$	$1$	$1$	$46.170$	$\Q$	None	✓				118.2.a.b	$1$	$0$	$-1$	$-2$	$-2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}-2q^{5}+2q^{6}-q^{8}+\cdots$
5782.2.a.c	$5782$	$2$	5782.a	1.a	$1$	$1$	$1$	$46.170$	$\Q$	None	✓				826.2.a.a	$1$	$0$	$-1$	$-2$	$3$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+3q^{5}+2q^{6}-q^{8}+\cdots$
5782.2.a.d	$5782$	$2$	5782.a	1.a	$1$	$1$	$1$	$46.170$	$\Q$	None	✓				118.2.a.a	$1$	$1$	$-1$	$1$	$3$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-q^{8}+\cdots$
5782.2.a.e	$5782$	$2$	5782.a	1.a	$1$	$1$	$1$	$46.170$	$\Q$	None	✓				118.2.a.d	$1$	$0$	$1$	$-2$	$2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}+2q^{5}-2q^{6}+q^{8}+\cdots$
5782.2.a.f	$5782$	$2$	5782.a	1.a	$1$	$1$	$1$	$46.170$	$\Q$	None	✓				826.2.e.a	$1$	$0$	$1$	$-1$	$3$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+q^{8}+\cdots$
5782.2.a.g	$5782$	$2$	5782.a	1.a	$1$	$1$	$1$	$46.170$	$\Q$	None	✓	✓			5782.2.a.g	$1$	$0$	$1$	$0$	$-1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-3q^{9}-q^{10}+\cdots$
5782.2.a.h	$5782$	$2$	5782.a	1.a	$1$	$1$	$1$	$46.170$	$\Q$	None	✓	✓			5782.2.a.g	$1$	$1$	$1$	$0$	$1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots$
5782.2.a.i	$5782$	$2$	5782.a	1.a	$1$	$1$	$1$	$46.170$	$\Q$	None	✓				826.2.e.a	$1$	$0$	$1$	$1$	$-3$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{8}+\cdots$
5782.2.a.j	$5782$	$2$	5782.a	1.a	$1$	$1$	$1$	$46.170$	$\Q$	None	✓				118.2.a.c	$1$	$0$	$1$	$1$	$-1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
5782.2.a.k	$5782$	$2$	5782.a	1.a	$1$	$2$	$2$	$46.170$	$\Q(\sqrt{13}) $	None	✓				826.2.a.d	$1$	$1$	$-2$	$-3$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots$
5782.2.a.l	$5782$	$2$	5782.a	1.a	$1$	$2$	$2$	$46.170$	$\Q(\sqrt{5}) $	None	✓				826.2.a.c	$1$	$0$	$-2$	$3$	$-2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta )q^{3}+q^{4}+(-2+2\beta )q^{5}+\cdots$
5782.2.a.m	$5782$	$2$	5782.a	1.a	$1$	$2$	$2$	$46.170$	$\Q(\sqrt{2}) $	None	✓	✓			5782.2.a.m	$1$	$1$	$2$	$-4$	$-2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-2+\beta )q^{3}+q^{4}-q^{5}+(-2+\cdots)q^{6}+\cdots$
5782.2.a.n	$5782$	$2$	5782.a	1.a	$1$	$2$	$2$	$46.170$	$\Q(\sqrt{5}) $	None	✓				826.2.a.f	$1$	$1$	$2$	$1$	$2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+(2-2\beta )q^{5}+\beta q^{6}+\cdots$
5782.2.a.o	$5782$	$2$	5782.a	1.a	$1$	$2$	$2$	$46.170$	$\Q(\sqrt{5}) $	None	✓				826.2.a.e	$1$	$0$	$2$	$3$	$4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}+q^{4}+2q^{5}+(1+\beta )q^{6}+\cdots$
5782.2.a.p	$5782$	$2$	5782.a	1.a	$1$	$2$	$2$	$46.170$	$\Q(\sqrt{2}) $	None	✓	✓			5782.2.a.m	$1$	$0$	$2$	$4$	$2$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(2+\beta )q^{3}+q^{4}+q^{5}+(2+\beta )q^{6}+\cdots$
5782.2.a.q	$5782$	$2$	5782.a	1.a	$1$	$4$	$4$	$46.170$	4.4.8768.1	None	✓				826.2.a.h	$1$	$1$	$-4$	$2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots$
5782.2.a.r	$5782$	$2$	5782.a	1.a	$1$	$4$	$4$	$46.170$	$\Q(\sqrt{3}, \sqrt{5})$	None	✓				826.2.a.g	$1$	$0$	$-4$	$2$	$6$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-\beta _{2}-\beta _{3})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
5782.2.a.s	$5782$	$2$	5782.a	1.a	$1$	$5$	$5$	$46.170$	5.5.1129264.1	None	✓				826.2.a.i	$1$	$1$	$5$	$-2$	$-5$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1-\beta _{3})q^{5}+\cdots$
5782.2.a.t	$5782$	$2$	5782.a	1.a	$1$	$6$	$6$	$46.170$	6.6.54148944.1	None	✓	✓			5782.2.a.t	$1$	$1$	$6$	$-5$	$-6$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{5})q^{5}+\cdots$
5782.2.a.u	$5782$	$2$	5782.a	1.a	$1$	$6$	$6$	$46.170$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓				826.2.a.j	$1$	$0$	$6$	$2$	$-3$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{5}q^{5}+\beta _{1}q^{6}+\cdots$
5782.2.a.v	$5782$	$2$	5782.a	1.a	$1$	$6$	$6$	$46.170$	6.6.54148944.1	None	✓	✓			5782.2.a.t	$1$	$0$	$6$	$5$	$6$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1+\beta _{5})q^{5}+\cdots$
5782.2.a.w	$5782$	$2$	5782.a	1.a	$1$	$7$	$7$	$46.170$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓		✓		826.2.e.b	$1$	$1$	$7$	$-1$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots$
5782.2.a.x	$5782$	$2$	5782.a	1.a	$1$	$7$	$7$	$46.170$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓				826.2.e.b	$1$	$1$	$7$	$1$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$
5782.2.a.y	$5782$	$2$	5782.a	1.a	$1$	$8$	$8$	$46.170$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓			5782.2.a.y	$1$	$1$	$-8$	$-3$	$-5$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots$
5782.2.a.z	$5782$	$2$	5782.a	1.a	$1$	$8$	$8$	$46.170$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓			5782.2.a.y	$1$	$0$	$-8$	$3$	$5$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{2})q^{5}-\beta _{1}q^{6}+\cdots$
5782.2.a.ba	$5782$	$2$	5782.a	1.a	$1$	$10$	$10$	$46.170$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓				826.2.e.d	$1$	$1$	$-10$	$-1$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{7}q^{5}+\beta _{1}q^{6}+\cdots$
5782.2.a.bb	$5782$	$2$	5782.a	1.a	$1$	$10$	$10$	$46.170$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓				826.2.e.c	$1$	$0$	$-10$	$-1$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots$
5782.2.a.bc	$5782$	$2$	5782.a	1.a	$1$	$10$	$10$	$46.170$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓		✓		826.2.e.d	$1$	$1$	$-10$	$1$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{7}q^{5}-\beta _{1}q^{6}+\cdots$
5782.2.a.bd	$5782$	$2$	5782.a	1.a	$1$	$10$	$10$	$46.170$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓		✓		826.2.e.c	$1$	$0$	$-10$	$1$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots$
5782.2.a.be	$5782$	$2$	5782.a	1.a	$1$	$12$	$12$	$46.170$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓		5782.2.a.be	$1$	$1$	$12$	$-6$	$-8$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{7}+\cdots)q^{5}+\cdots$
5782.2.a.bf	$5782$	$2$	5782.a	1.a	$1$	$12$	$12$	$46.170$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓		✓		826.2.e.e	$1$	$0$	$12$	$0$	$-3$	$0$	$-$	$-$	$-$	$-$	$3$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{8}q^{5}-\beta _{1}q^{6}+\cdots$
5782.2.a.bg	$5782$	$2$	5782.a	1.a	$1$	$12$	$12$	$46.170$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓				826.2.e.e	$1$	$0$	$12$	$0$	$3$	$0$	$-$	$+$	$+$	$-$	$3$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{8}q^{5}+\beta _{1}q^{6}+\cdots$
5782.2.a.bh	$5782$	$2$	5782.a	1.a	$1$	$12$	$12$	$46.170$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓			5782.2.a.be	$1$	$0$	$12$	$6$	$8$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1+\beta _{7})q^{5}+\cdots$
5782.2.a.bi	$5782$	$2$	5782.a	1.a	$1$	$14$	$14$	$46.170$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	✓	✓		5782.2.a.bi	$1$	$1$	$-14$	$-6$	$-10$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{9})q^{5}+\cdots$
5782.2.a.bj	$5782$	$2$	5782.a	1.a	$1$	$14$	$14$	$46.170$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	✓	✓		5782.2.a.bi	$1$	$0$	$-14$	$6$	$10$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{9})q^{5}-\beta _{1}q^{6}+\cdots$

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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.