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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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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
3330.2.a.a	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-3q^{7}-q^{8}+q^{10}+\cdots$
3330.2.a.b	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$-1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-3q^{7}-q^{8}+q^{10}+\cdots$
3330.2.a.c	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots$
3330.2.a.d	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots$
3330.2.a.e	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+3q^{7}-q^{8}+q^{10}+\cdots$
3330.2.a.f	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-5q^{7}-q^{8}-q^{10}+\cdots$
3330.2.a.g	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-3q^{7}-q^{8}-q^{10}+\cdots$
3330.2.a.h	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
3330.2.a.i	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-2q^{11}+\cdots$
3330.2.a.j	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+2q^{11}+\cdots$
3330.2.a.k	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+4q^{7}-q^{8}-q^{10}+\cdots$
3330.2.a.l	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+4q^{7}-q^{8}-q^{10}+\cdots$
3330.2.a.m	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots$
3330.2.a.n	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-3q^{7}+q^{8}-q^{10}+\cdots$
3330.2.a.o	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+2q^{11}+\cdots$
3330.2.a.p	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots$
3330.2.a.q	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+3q^{7}+q^{8}-q^{10}+\cdots$
3330.2.a.r	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-q^{10}+\cdots$
3330.2.a.s	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots$
3330.2.a.t	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-3q^{7}+q^{8}+q^{10}+\cdots$
3330.2.a.u	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$
3330.2.a.v	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$
3330.2.a.w	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+4q^{11}+\cdots$
3330.2.a.x	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots$
3330.2.a.y	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots$
3330.2.a.z	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+3q^{7}+q^{8}+q^{10}+\cdots$
3330.2.a.ba	$3330$	$2$	3330.a	1.a	$1$	$1$	$1$	$26.590$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+4q^{7}+q^{8}+q^{10}+\cdots$
3330.2.a.bb	$3330$	$2$	3330.a	1.a	$1$	$2$	$2$	$26.590$	$\Q(\sqrt{33}) $	None	✓	$1$	$1$	$-2$	$0$	$-2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+(-1-\beta )q^{7}-q^{8}+\cdots$
3330.2.a.bc	$3330$	$2$	3330.a	1.a	$1$	$2$	$2$	$26.590$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$-2$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
3330.2.a.bd	$3330$	$2$	3330.a	1.a	$1$	$2$	$2$	$26.590$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$0$	$-2$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+(-3+\beta )q^{7}+q^{8}+\cdots$
3330.2.a.be	$3330$	$2$	3330.a	1.a	$1$	$2$	$2$	$26.590$	$\Q(\sqrt{33}) $	None	✓	$1$	$1$	$2$	$0$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-\beta q^{7}+q^{8}-q^{10}+\cdots$
3330.2.a.bf	$3330$	$2$	3330.a	1.a	$1$	$2$	$2$	$26.590$	$\Q(\sqrt{113}) $	None	✓	$1$	$0$	$2$	$0$	$-2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+3q^{7}+q^{8}-q^{10}+\cdots$
3330.2.a.bg	$3330$	$2$	3330.a	1.a	$1$	$3$	$3$	$26.590$	3.3.892.1	None	✓	$1$	$1$	$-3$	$0$	$3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-\beta _{1}q^{7}-q^{8}-q^{10}+\cdots$
3330.2.a.bh	$3330$	$2$	3330.a	1.a	$1$	$3$	$3$	$26.590$	3.3.316.1	None	✓	$1$	$0$	$-3$	$0$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+(-1+2\beta _{1})q^{7}+\cdots$
3330.2.a.bi	$3330$	$2$	3330.a	1.a	$1$	$3$	$3$	$26.590$	3.3.316.1	None	✓	$1$	$0$	$3$	$0$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+(-1+2\beta _{1})q^{7}+\cdots$
3330.2.a.bj	$3330$	$2$	3330.a	1.a	$1$	$4$	$4$	$26.590$	4.4.54764.1	None	✓	$1$	$0$	$-4$	$0$	$-4$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+(1+\beta _{2})q^{7}-q^{8}+\cdots$
3330.2.a.bk	$3330$	$2$	3330.a	1.a	$1$	$5$	$5$	$26.590$	5.5.23544108.1	None	✓	$1$	$0$	$-5$	$0$	$-5$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+(1+\beta _{4})q^{7}-q^{8}+\cdots$
3330.2.a.bl	$3330$	$2$	3330.a	1.a	$1$	$5$	$5$	$26.590$	5.5.23544108.1	None	✓	$1$	$0$	$5$	$0$	$5$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+(1+\beta _{4})q^{7}+q^{8}+\cdots$
3330.2.d.a	$3330$	$2$	3330.d	5.b	$2$	$2$	$2$	$26.590$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}+(-2+i)q^{5}+2iq^{7}+\cdots$
3330.2.d.b	$3330$	$2$	3330.d	5.b	$2$	$2$	$2$	$26.590$	$\Q(\sqrt{-1}) $	None		$2$	$1$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-q^{4}+(-2+i)q^{5}+2iq^{7}+\cdots$
3330.2.d.c	$3330$	$2$	3330.d	5.b	$2$	$2$	$2$	$26.590$	$\Q(\sqrt{-1}) $	None		$2$	$1$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-q^{4}+(-1-2i)q^{5}+iq^{7}+\cdots$
3330.2.d.d	$3330$	$2$	3330.d	5.b	$2$	$2$	$2$	$26.590$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-q^{4}+(-1+2i)q^{5}+iq^{7}+\cdots$
3330.2.d.e	$3330$	$2$	3330.d	5.b	$2$	$2$	$2$	$26.590$	$\Q(\sqrt{-1}) $	None		$2$	$1$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}+(1-2i)q^{5}+5iq^{7}+\cdots$
3330.2.d.f	$3330$	$2$	3330.d	5.b	$2$	$2$	$2$	$26.590$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}+(2-i)q^{5}+2iq^{7}-iq^{8}+\cdots$
3330.2.d.g	$3330$	$2$	3330.d	5.b	$2$	$2$	$2$	$26.590$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-q^{4}+(2+i)q^{5}+2iq^{7}+iq^{8}+\cdots$
3330.2.d.h	$3330$	$2$	3330.d	5.b	$2$	$4$	$4$	$26.590$	$\Q(i, \sqrt{6})$	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-q^{4}+(-1-\beta _{2}-\beta _{3})q^{5}+\cdots$
3330.2.d.i	$3330$	$2$	3330.d	5.b	$2$	$4$	$4$	$26.590$	$\Q(\zeta_{12})$	None		$2$	$0$	$0$	$0$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{12}q^{2}-q^{4}+(-1-2\zeta_{12})q^{5}+\cdots$
3330.2.d.j	$3330$	$2$	3330.d	5.b	$2$	$4$	$4$	$26.590$	$\Q(i, \sqrt{5})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}-2\beta _{1}q^{7}-\beta _{1}q^{8}+\cdots$
3330.2.d.k	$3330$	$2$	3330.d	5.b	$2$	$4$	$4$	$26.590$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{8}^{2}q^{2}-q^{4}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+(\zeta_{8}+\cdots)q^{7}+\cdots$
3330.2.d.l	$3330$	$2$	3330.d	5.b	$2$	$4$	$4$	$26.590$	$\Q(\zeta_{12})$	None		$2$	$0$	$0$	$0$	$4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{12}q^{2}-q^{4}+(1+2\zeta_{12})q^{5}+(\zeta_{12}+\cdots)q^{7}+\cdots$

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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.