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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 (27 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4014.2.a.a	$4014$	$2$	4014.a	1.a	$1$	$1$	$1$	$32.052$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}+2q^{11}+\cdots$
4014.2.a.b	$4014$	$2$	4014.a	1.a	$1$	$1$	$1$	$32.052$	$\Q$	None	✓	$1$	$2$	$-1$	$0$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots$
4014.2.a.c	$4014$	$2$	4014.a	1.a	$1$	$1$	$1$	$32.052$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}+2q^{11}+4q^{13}+\cdots$
4014.2.a.d	$4014$	$2$	4014.a	1.a	$1$	$1$	$1$	$32.052$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-2q^{7}-q^{8}-2q^{10}+\cdots$
4014.2.a.e	$4014$	$2$	4014.a	1.a	$1$	$1$	$1$	$32.052$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-q^{11}-2q^{13}+q^{16}+\cdots$
4014.2.a.f	$4014$	$2$	4014.a	1.a	$1$	$1$	$1$	$32.052$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots$
4014.2.a.g	$4014$	$2$	4014.a	1.a	$1$	$1$	$1$	$32.052$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-2q^{11}+\cdots$
4014.2.a.h	$4014$	$2$	4014.a	1.a	$1$	$1$	$1$	$32.052$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}+4q^{13}+\cdots$
4014.2.a.i	$4014$	$2$	4014.a	1.a	$1$	$1$	$1$	$32.052$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{5}-4q^{7}+q^{8}+4q^{10}+\cdots$
4014.2.a.j	$4014$	$2$	4014.a	1.a	$1$	$2$	$2$	$32.052$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$-2$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2\beta q^{7}-q^{8}+(-5+\beta )q^{11}+\cdots$
4014.2.a.k	$4014$	$2$	4014.a	1.a	$1$	$2$	$2$	$32.052$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2\beta q^{5}+q^{8}-2\beta q^{10}+\cdots$
4014.2.a.l	$4014$	$2$	4014.a	1.a	$1$	$2$	$2$	$32.052$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$2$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2\beta q^{7}+q^{8}+(5-\beta )q^{11}+\cdots$
4014.2.a.m	$4014$	$2$	4014.a	1.a	$1$	$3$	$3$	$32.052$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$-3$	$0$	$3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta _{1})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
4014.2.a.n	$4014$	$2$	4014.a	1.a	$1$	$3$	$3$	$32.052$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$-3$	$0$	$7$	$-9$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(2+\beta _{1})q^{5}+(-3+\beta _{1}+\cdots)q^{7}+\cdots$
4014.2.a.o	$4014$	$2$	4014.a	1.a	$1$	$3$	$3$	$32.052$	3.3.257.1	None	✓	$1$	$0$	$3$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{1}q^{5}+(\beta _{1}+\beta _{2})q^{7}+\cdots$
4014.2.a.p	$4014$	$2$	4014.a	1.a	$1$	$3$	$3$	$32.052$	3.3.473.1	None	✓	$1$	$0$	$3$	$0$	$1$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{2}q^{5}+(3-\beta _{1})q^{7}+q^{8}+\cdots$
4014.2.a.q	$4014$	$2$	4014.a	1.a	$1$	$4$	$4$	$32.052$	4.4.10273.1	None	✓	$1$	$1$	$4$	$0$	$-2$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(-1-\beta _{3})q^{7}+\cdots$
4014.2.a.r	$4014$	$2$	4014.a	1.a	$1$	$5$	$5$	$32.052$	5.5.356173.1	None	✓	$1$	$1$	$5$	$0$	$-5$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
4014.2.a.s	$4014$	$2$	4014.a	1.a	$1$	$6$	$6$	$32.052$	6.6.232773917.1	None	✓	$1$	$1$	$-6$	$0$	$-6$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots$
4014.2.a.t	$4014$	$2$	4014.a	1.a	$1$	$6$	$6$	$32.052$	6.6.103354048.1	None	✓	$1$	$1$	$-6$	$0$	$-2$	$8$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(\beta _{4}-\beta _{5})q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots$
4014.2.a.u	$4014$	$2$	4014.a	1.a	$1$	$6$	$6$	$32.052$	6.6.103354048.1	None	✓	$1$	$0$	$6$	$0$	$2$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-\beta _{4}+\beta _{5})q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots$
4014.2.a.v	$4014$	$2$	4014.a	1.a	$1$	$7$	$7$	$32.052$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$-7$	$0$	$-6$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta _{4})q^{5}-\beta _{3}q^{7}+\cdots$
4014.2.a.w	$4014$	$2$	4014.a	1.a	$1$	$7$	$7$	$32.052$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$-7$	$0$	$-2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{3}q^{5}+(1-\beta _{2}+\beta _{6})q^{7}+\cdots$
4014.2.a.x	$4014$	$2$	4014.a	1.a	$1$	$8$	$8$	$32.052$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$-8$	$0$	$6$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta _{5}-\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots$
4014.2.a.y	$4014$	$2$	4014.a	1.a	$1$	$8$	$8$	$32.052$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$8$	$0$	$-6$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{5}+\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots$
4014.2.a.z	$4014$	$2$	4014.a	1.a	$1$	$8$	$8$	$32.052$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$8$	$0$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta _{3})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
4014.2.d.a	$4014$	$2$	4014.d	669.c	$2$	$72$	$72$	$32.052$		None		$4$	$0$	$0$	$0$	$0$	$16$			$\mathrm{SU}(2)[C_{2}]$

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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.