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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 (34 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	5	29	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5800.2.a.a	$5800$	$2$	5800.a	1.a	$1$	$1$	$1$	$46.313$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$0$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-4q^{7}+q^{9}-6q^{13}+8q^{21}+\cdots$
5800.2.a.b	$5800$	$2$	5800.a	1.a	$1$	$1$	$1$	$46.313$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$0$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{7}+q^{9}-6q^{11}-6q^{13}+\cdots$
5800.2.a.c	$5800$	$2$	5800.a	1.a	$1$	$1$	$1$	$46.313$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$0$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots$
5800.2.a.d	$5800$	$2$	5800.a	1.a	$1$	$1$	$1$	$46.313$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$0$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+4q^{7}+q^{9}+2q^{13}+4q^{17}+\cdots$
5800.2.a.e	$5800$	$2$	5800.a	1.a	$1$	$1$	$1$	$46.313$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}-2q^{9}+3q^{11}+q^{13}+\cdots$
5800.2.a.f	$5800$	$2$	5800.a	1.a	$1$	$1$	$1$	$46.313$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{9}+5q^{11}-4q^{13}-3q^{17}+\cdots$
5800.2.a.g	$5800$	$2$	5800.a	1.a	$1$	$1$	$1$	$46.313$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-3q^{9}+6q^{17}-4q^{19}+6q^{23}+\cdots$
5800.2.a.h	$5800$	$2$	5800.a	1.a	$1$	$1$	$1$	$46.313$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{9}+2q^{13}+6q^{17}-8q^{19}+q^{29}+\cdots$
5800.2.a.i	$5800$	$2$	5800.a	1.a	$1$	$1$	$1$	$46.313$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-3q^{9}-6q^{17}-4q^{19}-6q^{23}+\cdots$
5800.2.a.j	$5800$	$2$	5800.a	1.a	$1$	$1$	$1$	$46.313$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}-2q^{9}-3q^{11}+5q^{13}+\cdots$
5800.2.a.k	$5800$	$2$	5800.a	1.a	$1$	$1$	$1$	$46.313$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{9}+5q^{11}+4q^{13}+3q^{17}+\cdots$
5800.2.a.l	$5800$	$2$	5800.a	1.a	$1$	$1$	$1$	$46.313$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$0$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{7}+q^{9}-6q^{11}+6q^{13}+\cdots$
5800.2.a.m	$5800$	$2$	5800.a	1.a	$1$	$1$	$1$	$46.313$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$0$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots$
5800.2.a.n	$5800$	$2$	5800.a	1.a	$1$	$1$	$1$	$46.313$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}+4q^{11}+2q^{13}+4q^{19}+\cdots$
5800.2.a.o	$5800$	$2$	5800.a	1.a	$1$	$2$	$2$	$46.313$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$8$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+4q^{7}+2\beta q^{9}+(-1+\beta )q^{11}+\cdots$
5800.2.a.p	$5800$	$2$	5800.a	1.a	$1$	$3$	$3$	$46.313$	3.3.568.1	None	✓	$1$	$1$	$0$	$-2$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(2+\beta _{2})q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots$
5800.2.a.q	$5800$	$2$	5800.a	1.a	$1$	$3$	$3$	$46.313$	3.3.229.1	None	✓	$1$	$1$	$0$	$-1$	$0$	$3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(1-\beta _{1})q^{7}+(\beta _{1}-2\beta _{2})q^{9}+\cdots$
5800.2.a.r	$5800$	$2$	5800.a	1.a	$1$	$3$	$3$	$46.313$	3.3.148.1	None	✓	$1$	$0$	$0$	$2$	$0$	$-2$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-1+\beta _{2})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
5800.2.a.s	$5800$	$2$	5800.a	1.a	$1$	$3$	$3$	$46.313$	3.3.148.1	None	✓	$1$	$1$	$0$	$2$	$0$	$4$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1+\beta _{1})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
5800.2.a.t	$5800$	$2$	5800.a	1.a	$1$	$5$	$5$	$46.313$	5.5.580484.1	None	✓	$1$	$0$	$0$	$-3$	$0$	$-7$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{3}+(-1+\beta _{2}-\beta _{3})q^{7}+\cdots$
5800.2.a.u	$5800$	$2$	5800.a	1.a	$1$	$5$	$5$	$46.313$	5.5.3145252.1	None	✓	$1$	$1$	$0$	$1$	$0$	$-7$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+(-1+\beta _{2})q^{7}+(2-\beta _{2}+\beta _{4})q^{9}+\cdots$
5800.2.a.v	$5800$	$2$	5800.a	1.a	$1$	$5$	$5$	$46.313$	5.5.6083172.1	None	✓	$1$	$0$	$0$	$1$	$0$	$1$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(\beta _{2}-\beta _{3})q^{7}+(2+\beta _{2})q^{9}+\cdots$
5800.2.a.w	$5800$	$2$	5800.a	1.a	$1$	$6$	$6$	$46.313$	6.6.15523969.1	None	✓	$1$	$1$	$0$	$-2$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+(-\beta _{1}+\beta _{3}+\beta _{4}+\beta _{5})q^{7}+\cdots$
5800.2.a.x	$5800$	$2$	5800.a	1.a	$1$	$6$	$6$	$46.313$	6.6.16196689.1	None	✓	$1$	$1$	$0$	$-1$	$0$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(-1+\beta _{1}-\beta _{3})q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots$
5800.2.a.y	$5800$	$2$	5800.a	1.a	$1$	$6$	$6$	$46.313$	6.6.16196689.1	None	✓	$1$	$1$	$0$	$1$	$0$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(1-\beta _{1}+\beta _{3})q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots$
5800.2.a.z	$5800$	$2$	5800.a	1.a	$1$	$6$	$6$	$46.313$	6.6.15523969.1	None	✓	$1$	$1$	$0$	$2$	$0$	$4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+(\beta _{1}-\beta _{3}-\beta _{4}-\beta _{5})q^{7}+\cdots$
5800.2.a.ba	$5800$	$2$	5800.a	1.a	$1$	$7$	$7$	$46.313$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$-2$	$0$	$8$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1-\beta _{1}+\beta _{2})q^{7}+(1+\beta _{4}+\cdots)q^{9}+\cdots$
5800.2.a.bb	$5800$	$2$	5800.a	1.a	$1$	$7$	$7$	$46.313$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$0$	$0$	$-6$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{6})q^{7}+(2+\beta _{2})q^{9}+\cdots$
5800.2.a.bc	$5800$	$2$	5800.a	1.a	$1$	$7$	$7$	$46.313$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$0$	$0$	$6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1+\beta _{6})q^{7}+(2+\beta _{2})q^{9}+\cdots$
5800.2.a.bd	$5800$	$2$	5800.a	1.a	$1$	$7$	$7$	$46.313$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$0$	$2$	$0$	$-8$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{7}+(1+\beta _{4}+\cdots)q^{9}+\cdots$
5800.2.a.be	$5800$	$2$	5800.a	1.a	$1$	$8$	$8$	$46.313$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$0$	$-3$	$0$	$-3$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{6}q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots$
5800.2.a.bf	$5800$	$2$	5800.a	1.a	$1$	$8$	$8$	$46.313$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$0$	$3$	$0$	$3$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{6}q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots$
5800.2.a.bg	$5800$	$2$	5800.a	1.a	$1$	$11$	$11$	$46.313$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$1$	$0$	$-5$	$0$	$-1$	$-$	$-$	$+$	$+$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{10}q^{7}+(\beta _{1}+\beta _{3}+\beta _{4}+\cdots)q^{9}+\cdots$
5800.2.a.bh	$5800$	$2$	5800.a	1.a	$1$	$11$	$11$	$46.313$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$0$	$5$	$0$	$1$	$+$	$-$	$+$	$-$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{10}q^{7}+(\beta _{1}+\beta _{3}+\beta _{4}+\cdots)q^{9}+\cdots$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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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.