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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 (27 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	5	29	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4640.2.a.a	$4640$	$2$	4640.a	1.a	$1$	$1$	$1$	$37.051$	$\Q$	None	✓	✓			4640.2.a.a	$1$	$0$	$0$	$-2$	$-1$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots$
4640.2.a.b	$4640$	$2$	4640.a	1.a	$1$	$1$	$1$	$37.051$	$\Q$	None	✓	✓			4640.2.a.b	$1$	$1$	$0$	$-2$	$1$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots$
4640.2.a.c	$4640$	$2$	4640.a	1.a	$1$	$1$	$1$	$37.051$	$\Q$	None	✓	✓			4640.2.a.c	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}-3q^{9}+2q^{11}+2q^{13}+\cdots$
4640.2.a.d	$4640$	$2$	4640.a	1.a	$1$	$1$	$1$	$37.051$	$\Q$	None	✓	✓			4640.2.a.c	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-3q^{9}-2q^{11}+2q^{13}+\cdots$
4640.2.a.e	$4640$	$2$	4640.a	1.a	$1$	$1$	$1$	$37.051$	$\Q$	None	✓	✓			4640.2.a.a	$1$	$1$	$0$	$2$	$-1$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots$
4640.2.a.f	$4640$	$2$	4640.a	1.a	$1$	$1$	$1$	$37.051$	$\Q$	None	✓	✓			4640.2.a.b	$1$	$0$	$0$	$2$	$1$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots$
4640.2.a.g	$4640$	$2$	4640.a	1.a	$1$	$2$	$2$	$37.051$	$\Q(\sqrt{5}) $	None	✓	✓			4640.2.a.g	$1$	$0$	$0$	$-1$	$-2$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-q^{5}+(-1+3\beta )q^{7}+(-2+\cdots)q^{9}+\cdots$
4640.2.a.h	$4640$	$2$	4640.a	1.a	$1$	$2$	$2$	$37.051$	$\Q(\sqrt{2}) $	None	✓	✓			4640.2.a.h	$2$	$0$	$0$	$0$	$2$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{5}+\beta q^{7}-3q^{9}+\beta q^{11}-2q^{13}+\cdots$
4640.2.a.i	$4640$	$2$	4640.a	1.a	$1$	$2$	$2$	$37.051$	$\Q(\sqrt{5}) $	None	✓	✓			4640.2.a.g	$1$	$0$	$0$	$1$	$-2$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+(1-3\beta )q^{7}+(-2+\beta )q^{9}+\cdots$
4640.2.a.j	$4640$	$2$	4640.a	1.a	$1$	$3$	$3$	$37.051$	3.3.229.1	None	✓	✓			4640.2.a.j	$1$	$1$	$0$	$-3$	$-3$	$-7$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}-q^{5}+(-2-2\beta _{1}+\cdots)q^{7}+\cdots$
4640.2.a.k	$4640$	$2$	4640.a	1.a	$1$	$3$	$3$	$37.051$	3.3.229.1	None	✓	✓			4640.2.a.j	$1$	$0$	$0$	$3$	$-3$	$7$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}-q^{5}+(2+2\beta _{1}-\beta _{2})q^{7}+\cdots$
4640.2.a.l	$4640$	$2$	4640.a	1.a	$1$	$4$	$4$	$37.051$	4.4.11344.1	None	✓	✓			4640.2.a.l	$1$	$1$	$0$	$-2$	$-4$	$2$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}-q^{5}-\beta _{3}q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$
4640.2.a.m	$4640$	$2$	4640.a	1.a	$1$	$4$	$4$	$37.051$	$\Q(\zeta_{24})^+$	None	✓	✓			4640.2.a.m	$2$	$1$	$0$	$0$	$-4$	$0$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-q^{5}+\beta _{2}q^{7}-q^{9}+\beta _{3}q^{11}+\cdots$
4640.2.a.n	$4640$	$2$	4640.a	1.a	$1$	$4$	$4$	$37.051$	$\Q(\sqrt{6}, \sqrt{10})$	None	✓	✓			4640.2.a.n	$2$	$1$	$0$	$0$	$-4$	$0$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-q^{5}-\beta _{3}q^{7}+3q^{9}+\beta _{3}q^{11}+\cdots$
4640.2.a.o	$4640$	$2$	4640.a	1.a	$1$	$4$	$4$	$37.051$	$\Q(\sqrt{6}, \sqrt{26})$	None	✓	✓			4640.2.a.o	$2$	$0$	$0$	$0$	$-4$	$0$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}-\beta _{1}q^{7}+3q^{9}+\beta _{2}q^{11}+\cdots$
4640.2.a.p	$4640$	$2$	4640.a	1.a	$1$	$4$	$4$	$37.051$	$\Q(\zeta_{24})^+$	None	✓	✓			4640.2.a.p	$2$	$1$	$0$	$0$	$4$	$0$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+q^{5}-\beta _{2}q^{7}-q^{9}+\beta _{2}q^{11}+\cdots$
4640.2.a.q	$4640$	$2$	4640.a	1.a	$1$	$4$	$4$	$37.051$	$\Q(\zeta_{24})^+$	None	✓	✓			4640.2.a.q	$2$	$1$	$0$	$0$	$4$	$0$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+q^{5}+\beta _{3}q^{7}-q^{9}-\beta _{2}q^{11}+\cdots$
4640.2.a.r	$4640$	$2$	4640.a	1.a	$1$	$4$	$4$	$37.051$	4.4.11344.1	None	✓	✓			4640.2.a.l	$1$	$0$	$0$	$2$	$-4$	$-2$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}-q^{5}+\beta _{3}q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$
4640.2.a.s	$4640$	$2$	4640.a	1.a	$1$	$6$	$6$	$37.051$	6.6.26118032.1	None	✓	✓	✓		4640.2.a.s	$1$	$1$	$0$	$-1$	$-6$	$-3$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots$
4640.2.a.t	$4640$	$2$	4640.a	1.a	$1$	$6$	$6$	$37.051$	6.6.39643024.1	None	✓	✓	✓		4640.2.a.t	$1$	$1$	$0$	$-1$	$6$	$-5$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+q^{5}+(-1-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots$
4640.2.a.u	$4640$	$2$	4640.a	1.a	$1$	$6$	$6$	$37.051$	6.6.26118032.1	None	✓	✓			4640.2.a.s	$1$	$0$	$0$	$1$	$-6$	$3$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots$
4640.2.a.v	$4640$	$2$	4640.a	1.a	$1$	$6$	$6$	$37.051$	6.6.39643024.1	None	✓	✓			4640.2.a.t	$1$	$0$	$0$	$1$	$6$	$5$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}+(1+\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots$
4640.2.a.w	$4640$	$2$	4640.a	1.a	$1$	$7$	$7$	$37.051$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓		4640.2.a.w	$1$	$1$	$0$	$-1$	$7$	$-1$	$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+q^{5}+(\beta _{1}-\beta _{5})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
4640.2.a.x	$4640$	$2$	4640.a	1.a	$1$	$7$	$7$	$37.051$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓			4640.2.a.w	$1$	$0$	$0$	$1$	$7$	$1$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}+(-\beta _{1}+\beta _{5})q^{7}+(1+\cdots)q^{9}+\cdots$
4640.2.a.y	$4640$	$2$	4640.a	1.a	$1$	$8$	$8$	$37.051$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓		4640.2.a.y	$2$	$0$	$0$	$0$	$8$	$0$	$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}+(\beta _{1}+\beta _{5})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots$
4640.2.a.z	$4640$	$2$	4640.a	1.a	$1$	$10$	$10$	$37.051$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓		4640.2.a.z	$2$	$0$	$0$	$0$	$-10$	$0$	$-$	$+$	$+$	$-$	$2^{6}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+\beta _{9}q^{7}+(2+\beta _{2})q^{9}+\cdots$
4640.2.a.ba	$4640$	$2$	4640.a	1.a	$1$	$10$	$10$	$37.051$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓		4640.2.a.ba	$2$	$0$	$0$	$0$	$10$	$0$	$-$	$-$	$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}-\beta _{7}q^{7}+(3+\beta _{2})q^{9}+\cdots$

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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.