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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	Image	CM	RM	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	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
660.1.v.a	$660$	$1$	660.v	165.l	$4$	$4$	$2$	$0.329$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{3}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{3}q^{11}+\cdots$
660.1.v.b	$660$	$1$	660.v	165.l	$4$	$4$	$2$	$0.329$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+\zeta_{12}^{2}q^{3}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{4}q^{9}+\cdots$
660.2.a.a	$660$	$2$	660.a	1.a	$1$	$1$	$1$	$5.270$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$
660.2.a.b	$660$	$2$	660.a	1.a	$1$	$1$	$1$	$5.270$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}+q^{11}-4q^{13}+q^{15}+\cdots$
660.2.a.c	$660$	$2$	660.a	1.a	$1$	$1$	$1$	$5.270$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-4q^{7}+q^{9}-q^{11}-4q^{13}+\cdots$
660.2.a.d	$660$	$2$	660.a	1.a	$1$	$1$	$1$	$5.270$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+2q^{7}+q^{9}+q^{11}+2q^{13}+\cdots$
660.2.a.e	$660$	$2$	660.a	1.a	$1$	$2$	$2$	$5.270$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+q^{11}+\cdots$
660.2.a.f	$660$	$2$	660.a	1.a	$1$	$2$	$2$	$5.270$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}-q^{11}+\cdots$
660.2.c.a	$660$	$2$	660.c	5.b	$2$	$2$	$2$	$5.270$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(-1+2i)q^{5}+2iq^{7}-q^{9}+\cdots$
660.2.c.b	$660$	$2$	660.c	5.b	$2$	$2$	$2$	$5.270$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(1-2i)q^{5}-q^{9}+q^{11}-4iq^{13}+\cdots$
660.2.c.c	$660$	$2$	660.c	5.b	$2$	$4$	$4$	$5.270$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{1}+\beta _{2})q^{7}-q^{9}+\cdots$
660.2.d.a	$660$	$2$	660.d	33.d	$2$	$16$	$16$	$5.270$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$4$	$0$	$0$		$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}+\beta _{10}q^{5}+\beta _{2}q^{7}+(-1-\beta _{6}+\cdots)q^{9}+\cdots$
660.2.f.a	$660$	$2$	660.f	12.b	$2$	$40$	$40$	$5.270$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
660.2.f.b	$660$	$2$	660.f	12.b	$2$	$40$	$40$	$5.270$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
660.2.i.a	$660$	$2$	660.i	220.g	$2$	$36$	$36$	$5.270$		$_{}$	None	None		$4$	$0$	$0$	$-36$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
660.2.i.b	$660$	$2$	660.i	220.g	$2$	$36$	$36$	$5.270$		$_{}$	None	None		$4$	$0$	$0$	$36$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
660.2.k.a	$660$	$2$	660.k	44.c	$2$	$4$	$4$	$5.270$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-2q^{4}-q^{5}+\zeta_{8}^{3}q^{6}+\cdots$
660.2.k.b	$660$	$2$	660.k	44.c	$2$	$4$	$4$	$5.270$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{3}q^{2}+\zeta_{8}q^{3}+2q^{4}+q^{5}+\zeta_{8}^{2}q^{6}+\cdots$
660.2.k.c	$660$	$2$	660.k	44.c	$2$	$20$	$20$	$5.270$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$20$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{9}q^{2}+\beta _{5}q^{3}-\beta _{2}q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
660.2.k.d	$660$	$2$	660.k	44.c	$2$	$20$	$20$	$5.270$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-20$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}-q^{5}+\beta _{17}q^{6}+\cdots$
660.2.l.a	$660$	$2$	660.l	60.h	$2$	$60$	$60$	$5.270$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
660.2.l.b	$660$	$2$	660.l	60.h	$2$	$60$	$60$	$5.270$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
660.2.n.a	$660$	$2$	660.n	165.d	$2$	$4$	$4$	$5.270$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-1$	$3$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+(1+\beta _{2}+\cdots)q^{9}+\cdots$
660.2.n.b	$660$	$2$	660.n	165.d	$2$	$4$	$4$	$5.270$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$1$	$-3$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}+(-1-\beta _{2}-\beta _{3})q^{5}+(1+\beta _{2}+\cdots)q^{9}+\cdots$
660.2.n.c	$660$	$2$	660.n	165.d	$2$	$16$	$16$	$5.270$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{3}+(\beta _{2}-\beta _{4})q^{5}+\beta _{9}q^{7}+(-1+\cdots)q^{9}+\cdots$
660.2.q.a	$660$	$2$	660.q	660.q	$4$	$272$	$136$	$5.270$		$_{}$	None	None		$16$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
660.2.t.a	$660$	$2$	660.t	15.e	$4$	$20$	$10$	$5.270$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{9}q^{3}-\beta _{11}q^{5}+(-\beta _{4}+\beta _{6}+\beta _{7}+\cdots)q^{7}+\cdots$
660.2.t.b	$660$	$2$	660.t	15.e	$4$	$20$	$10$	$5.270$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{3}+\beta _{10}q^{5}+(1+\beta _{2}-\beta _{14}+\cdots)q^{7}+\cdots$
660.2.u.a	$660$	$2$	660.u	20.e	$4$	$60$	$30$	$5.270$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
660.2.u.b	$660$	$2$	660.u	20.e	$4$	$60$	$30$	$5.270$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
660.2.x.a	$660$	$2$	660.x	55.e	$4$	$24$	$12$	$5.270$		$_{}$	None	None		$4$	$0$	$0$	$0$	$8$	$0$			$\mathrm{SU}(2)[C_{4}]$
660.2.y.a	$660$	$2$	660.y	11.c	$5$	$8$	$2$	$5.270$	8.0.13140625.1	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-2$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{3}-\beta _{4}-\beta _{7})q^{3}+\beta _{7}q^{5}+\cdots$
660.2.y.b	$660$	$2$	660.y	11.c	$5$	$8$	$2$	$5.270$	8.0.159390625.1	$_{}$	None	None		$2$	$0$	$0$	$-2$	$2$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{3}q^{3}+\beta _{6}q^{5}+(1-2\beta _{2}-2\beta _{3}+\cdots)q^{7}+\cdots$
660.2.y.c	$660$	$2$	660.y	11.c	$5$	$8$	$2$	$5.270$	8.0.819390625.1	$_{}$	None	None		$2$	$0$	$0$	$2$	$-2$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{2}+\beta _{3}-\beta _{6})q^{3}-\beta _{6}q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots$
660.2.y.d	$660$	$2$	660.y	11.c	$5$	$8$	$2$	$5.270$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$2$	$2$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{6}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots$
660.2.bb.a	$660$	$2$	660.bb	165.r	$10$	$96$	$24$	$5.270$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
660.2.bd.a	$660$	$2$	660.bd	660.ad	$10$	$544$	$136$	$5.270$		$_{}$	None	None		$16$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
660.2.be.a	$660$	$2$	660.be	44.g	$10$	$96$	$24$	$5.270$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-24$	$0$			$\mathrm{SU}(2)[C_{10}]$
660.2.be.b	$660$	$2$	660.be	44.g	$10$	$96$	$24$	$5.270$		$_{}$	None	None		$4$	$0$	$0$	$0$	$24$	$0$			$\mathrm{SU}(2)[C_{10}]$
660.2.bg.a	$660$	$2$	660.bg	220.o	$10$	$144$	$36$	$5.270$		$_{}$	None	None		$4$	$0$	$0$	$-36$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
660.2.bg.b	$660$	$2$	660.bg	220.o	$10$	$144$	$36$	$5.270$		$_{}$	None	None		$4$	$0$	$0$	$36$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
660.2.bj.a	$660$	$2$	660.bj	132.o	$10$	$384$	$96$	$5.270$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
660.2.bl.a	$660$	$2$	660.bl	33.f	$10$	$16$	$4$	$5.270$	16.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$-8$	$0$	$10$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-1+\beta _{2}-\beta _{8}+\beta _{10}-\beta _{12})q^{3}+\cdots$
660.2.bl.b	$660$	$2$	660.bl	33.f	$10$	$48$	$12$	$5.270$		$_{}$	None	None		$4$	$0$	$0$	$4$	$0$	$-10$			$\mathrm{SU}(2)[C_{10}]$
660.2.bm.a	$660$	$2$	660.bm	55.j	$10$	$48$	$12$	$5.270$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{10}]$
660.2.bo.a	$660$	$2$	660.bo	55.l	$20$	$96$	$12$	$5.270$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-8$	$-20$			$\mathrm{SU}(2)[C_{20}]$
660.2.br.a	$660$	$2$	660.br	220.v	$20$	$576$	$72$	$5.270$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{20}]$
660.2.bs.a	$660$	$2$	660.bs	165.v	$20$	$192$	$24$	$5.270$		$_{}$	None	None		$8$	$0$	$0$	$-2$	$0$	$8$			$\mathrm{SU}(2)[C_{20}]$
660.2.bv.a	$660$	$2$	660.bv	660.av	$20$	$1088$	$136$	$5.270$		$_{}$	None	None		$16$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{20}]$
660.3.b.a	$660$	$3$	660.b	11.b	$2$	$16$	$16$	$17.984$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}-\beta _{3}q^{5}-\beta _{7}q^{7}+3q^{9}+(-1+\cdots)q^{11}+\cdots$

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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.