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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 (21 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	3	269	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4842.2.a.a	$4842$	$2$	4842.a	1.a	$1$	$1$	$1$	$38.664$	$\Q$	None	✓	✓			4842.2.a.a	$1$	$0$	$-1$	$0$	$2$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}+2q^{7}-q^{8}-2q^{10}+\cdots$
4842.2.a.b	$4842$	$2$	4842.a	1.a	$1$	$1$	$1$	$38.664$	$\Q$	None	✓				1614.2.a.a	$1$	$0$	$1$	$0$	$-2$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}-4q^{7}+q^{8}-2q^{10}+\cdots$
4842.2.a.c	$4842$	$2$	4842.a	1.a	$1$	$1$	$1$	$38.664$	$\Q$	None	✓	✓			4842.2.a.a	$1$	$0$	$1$	$0$	$-2$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+2q^{7}+q^{8}-2q^{10}+\cdots$
4842.2.a.d	$4842$	$2$	4842.a	1.a	$1$	$2$	$2$	$38.664$	$\Q(\sqrt{13}) $	None	✓				538.2.a.b	$1$	$1$	$-2$	$0$	$-1$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta q^{5}-q^{7}-q^{8}+\beta q^{10}+\cdots$
4842.2.a.e	$4842$	$2$	4842.a	1.a	$1$	$2$	$2$	$38.664$	$\Q(\sqrt{5}) $	None	✓				1614.2.a.b	$1$	$0$	$-2$	$0$	$2$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2\beta q^{5}+(-1+3\beta )q^{7}+\cdots$
4842.2.a.f	$4842$	$2$	4842.a	1.a	$1$	$2$	$2$	$38.664$	$\Q(\sqrt{5}) $	None	✓				538.2.a.a	$1$	$0$	$-2$	$0$	$5$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(3-\beta )q^{5}+(-3+2\beta )q^{7}+\cdots$
4842.2.a.g	$4842$	$2$	4842.a	1.a	$1$	$3$	$3$	$38.664$	3.3.361.1	None	✓				1614.2.a.d	$1$	$0$	$-3$	$0$	$1$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1-\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots$
4842.2.a.h	$4842$	$2$	4842.a	1.a	$1$	$3$	$3$	$38.664$	$\Q(\zeta_{14})^+$	None	✓				1614.2.a.e	$1$	$1$	$-3$	$0$	$7$	$-6$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(2+\beta _{1})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots$
4842.2.a.i	$4842$	$2$	4842.a	1.a	$1$	$3$	$3$	$38.664$	$\Q(\zeta_{14})^+$	None	✓				1614.2.a.c	$1$	$1$	$3$	$0$	$1$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{1}q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+\cdots$
4842.2.a.j	$4842$	$2$	4842.a	1.a	$1$	$4$	$4$	$38.664$	4.4.4913.1	None	✓				538.2.a.c	$1$	$1$	$4$	$0$	$-5$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{1})q^{5}-\beta _{2}q^{7}+\cdots$
4842.2.a.k	$4842$	$2$	4842.a	1.a	$1$	$5$	$5$	$38.664$	5.5.459533.1	None	✓				1614.2.a.f	$1$	$0$	$5$	$0$	$5$	$5$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1+\beta _{1}+\beta _{4})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
4842.2.a.l	$4842$	$2$	4842.a	1.a	$1$	$6$	$6$	$38.664$	6.6.20228249.1	None	✓				1614.2.a.h	$1$	$1$	$-6$	$0$	$-6$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1+\beta _{2})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots$
4842.2.a.m	$4842$	$2$	4842.a	1.a	$1$	$6$	$6$	$38.664$	6.6.137144153.1	None	✓		✓		1614.2.a.g	$1$	$1$	$6$	$0$	$-6$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{3})q^{5}+(-1+\beta _{4}+\cdots)q^{7}+\cdots$
4842.2.a.n	$4842$	$2$	4842.a	1.a	$1$	$7$	$7$	$38.664$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓		✓		538.2.a.e	$1$	$1$	$-7$	$0$	$-7$	$6$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta _{4})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots$
4842.2.a.o	$4842$	$2$	4842.a	1.a	$1$	$7$	$7$	$38.664$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓				538.2.a.d	$1$	$0$	$7$	$0$	$6$	$-3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-\beta _{3}+\beta _{4})q^{5}+(-1+\cdots)q^{7}+\cdots$
4842.2.a.p	$4842$	$2$	4842.a	1.a	$1$	$8$	$8$	$38.664$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓		✓		1614.2.a.j	$1$	$0$	$-8$	$0$	$-4$	$9$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta _{5})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
4842.2.a.q	$4842$	$2$	4842.a	1.a	$1$	$8$	$8$	$38.664$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓		✓		1614.2.a.i	$1$	$0$	$8$	$0$	$0$	$9$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-\beta _{1}q^{5}+(1+\beta _{2})q^{7}+q^{8}+\cdots$
4842.2.a.r	$4842$	$2$	4842.a	1.a	$1$	$9$	$9$	$38.664$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓	✓	4842.2.a.r	$1$	$1$	$-9$	$0$	$5$	$-10$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1-\beta _{1})q^{5}+(-1+\beta _{5}+\cdots)q^{7}+\cdots$
4842.2.a.s	$4842$	$2$	4842.a	1.a	$1$	$9$	$9$	$38.664$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓	✓	4842.2.a.r	$1$	$1$	$9$	$0$	$-5$	$-10$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(-1+\beta _{5}+\cdots)q^{7}+\cdots$
4842.2.a.t	$4842$	$2$	4842.a	1.a	$1$	$13$	$13$	$38.664$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	✓	✓		4842.2.a.t	$1$	$0$	$-13$	$0$	$-5$	$6$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta _{1}q^{5}-\beta _{3}q^{7}-q^{8}+\cdots$
4842.2.a.u	$4842$	$2$	4842.a	1.a	$1$	$13$	$13$	$38.664$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	✓	✓		4842.2.a.t	$1$	$0$	$13$	$0$	$5$	$6$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{1}q^{5}-\beta _{3}q^{7}+q^{8}+\cdots$

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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.