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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 (20 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	7	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5054.2.a.c	$5054$	$2$	5054.a	1.a	$1$	$1$	$1$	$40.356$	$\Q$	None	✓	$1$	$0$	$1$	$2$	$0$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{7}+q^{8}+\cdots$
5054.2.a.f	$5054$	$2$	5054.a	1.a	$1$	$2$	$2$	$40.356$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$-1$	$2$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-q^{7}+\cdots$
5054.2.a.g	$5054$	$2$	5054.a	1.a	$1$	$2$	$2$	$40.356$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$1$	$-3$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}+(-1-\beta )q^{5}-\beta q^{6}+\cdots$
5054.2.a.i	$5054$	$2$	5054.a	1.a	$1$	$2$	$2$	$40.356$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$3$	$-4$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta )q^{3}+q^{4}+(-3+2\beta )q^{5}+\cdots$
5054.2.a.k	$5054$	$2$	5054.a	1.a	$1$	$2$	$2$	$40.356$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$-3$	$1$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta )q^{3}+q^{4}+(2-3\beta )q^{5}+\cdots$
5054.2.a.o	$5054$	$2$	5054.a	1.a	$1$	$2$	$2$	$40.356$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$1$	$-1$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+(1-3\beta )q^{5}+\beta q^{6}+\cdots$
5054.2.a.q	$5054$	$2$	5054.a	1.a	$1$	$3$	$3$	$40.356$	3.3.148.1	None	✓	$1$	$0$	$-3$	$-2$	$-1$	$-3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
5054.2.a.r	$5054$	$2$	5054.a	1.a	$1$	$3$	$3$	$40.356$	3.3.469.1	None	✓	$1$	$0$	$-3$	$1$	$5$	$-3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{2}q^{3}+q^{4}+(2-\beta _{1})q^{5}+\beta _{2}q^{6}+\cdots$
5054.2.a.u	$5054$	$2$	5054.a	1.a	$1$	$3$	$3$	$40.356$	3.3.148.1	None	✓	$1$	$0$	$3$	$2$	$-1$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
5054.2.a.w	$5054$	$2$	5054.a	1.a	$1$	$4$	$4$	$40.356$	4.4.151572.1	None	✓	$1$	$0$	$-4$	$-1$	$1$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots$
5054.2.a.x	$5054$	$2$	5054.a	1.a	$1$	$4$	$4$	$40.356$	4.4.151572.1	None	✓	$1$	$0$	$4$	$1$	$1$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots$
5054.2.a.y	$5054$	$2$	5054.a	1.a	$1$	$4$	$4$	$40.356$	$\Q(\zeta_{20})^+$	None	✓	$1$	$0$	$4$	$4$	$2$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta _{1})q^{3}+q^{4}+(-\beta _{2}-\beta _{3})q^{5}+\cdots$
5054.2.a.ba	$5054$	$2$	5054.a	1.a	$1$	$6$	$6$	$40.356$	6.6.48952000.1	None	✓	$1$	$0$	$-6$	$2$	$-5$	$-6$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots$
5054.2.a.be	$5054$	$2$	5054.a	1.a	$1$	$6$	$6$	$40.356$	6.6.36538000.1	None	✓	$1$	$0$	$6$	$0$	$-1$	$6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots$
5054.2.a.bg	$5054$	$2$	5054.a	1.a	$1$	$8$	$8$	$40.356$	8.8.$\cdots$.1	None	✓	$1$	$0$	$-8$	$4$	$-2$	$8$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta _{2}+\beta _{5})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
5054.2.a.bi	$5054$	$2$	5054.a	1.a	$1$	$8$	$8$	$40.356$	8.8.$\cdots$.1	None	✓	$1$	$0$	$8$	$4$	$6$	$-8$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta _{5}-\beta _{7})q^{3}+q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
5054.2.a.bj	$5054$	$2$	5054.a	1.a	$1$	$9$	$9$	$40.356$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$-9$	$-3$	$3$	$-9$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots$
5054.2.a.bk	$5054$	$2$	5054.a	1.a	$1$	$9$	$9$	$40.356$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$9$	$3$	$3$	$-9$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots$
5054.2.a.bl	$5054$	$2$	5054.a	1.a	$1$	$12$	$12$	$40.356$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$-12$	$-3$	$3$	$12$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+(\beta _{2}-\beta _{5})q^{5}+\cdots$
5054.2.a.bm	$5054$	$2$	5054.a	1.a	$1$	$12$	$12$	$40.356$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$12$	$3$	$3$	$12$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{2}-\beta _{5})q^{5}+\cdots$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
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.