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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
494.2.a.a	$494$	$2$	494.a	1.a	$1$	$1$	$1$	$3.945$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
494.2.a.b	$494$	$2$	494.a	1.a	$1$	$1$	$1$	$3.945$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}+4q^{7}-q^{8}-3q^{9}+\cdots$
494.2.a.c	$494$	$2$	494.a	1.a	$1$	$1$	$1$	$3.945$	$\Q$	None	✓	$1$	$0$	$-1$	$3$	$-3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-3q^{5}-3q^{6}+3q^{7}+\cdots$
494.2.a.d	$494$	$2$	494.a	1.a	$1$	$1$	$1$	$3.945$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-3q^{7}+\cdots$
494.2.a.e	$494$	$2$	494.a	1.a	$1$	$3$	$3$	$3.945$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$-3$	$-3$	$3$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-2\beta _{1}+\beta _{2})q^{3}+q^{4}+\cdots$
494.2.a.f	$494$	$2$	494.a	1.a	$1$	$3$	$3$	$3.945$	3.3.361.1	None	✓	$1$	$0$	$-3$	$-1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{2}q^{3}+q^{4}+(1-\beta _{1}-\beta _{2})q^{5}+\cdots$
494.2.a.g	$494$	$2$	494.a	1.a	$1$	$3$	$3$	$3.945$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$3$	$5$	$5$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(2-\beta _{1})q^{3}+q^{4}+(2+\beta _{2})q^{5}+\cdots$
494.2.a.h	$494$	$2$	494.a	1.a	$1$	$4$	$4$	$3.945$	4.4.16609.1	None	✓	$1$	$0$	$4$	$2$	$2$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{2}q^{3}+q^{4}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
494.2.d.a	$494$	$2$	494.d	13.b	$2$	$2$	$2$	$3.945$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{3}-q^{4}-3iq^{5}+iq^{6}+\cdots$
494.2.d.b	$494$	$2$	494.d	13.b	$2$	$6$	$6$	$3.945$	6.0.153664.1	None		$2$	$0$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+(-1-\beta _{2}+\beta _{4})q^{3}-q^{4}+\cdots$
494.2.d.c	$494$	$2$	494.d	13.b	$2$	$14$	$14$	$3.945$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		$2$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{2}+\beta _{5}q^{3}-q^{4}-\beta _{12}q^{5}+\beta _{1}q^{6}+\cdots$
494.2.e.a	$494$	$2$	494.e	247.e	$3$	$2$	$1$	$3.945$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$-3$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(-3+3\zeta_{6})q^{5}+\cdots$
494.2.e.b	$494$	$2$	494.e	247.e	$3$	$2$	$1$	$3.945$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(1-\zeta_{6})q^{5}+\cdots$
494.2.e.c	$494$	$2$	494.e	247.e	$3$	$18$	$9$	$3.945$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		$2$	$0$	$9$	$0$	$4$	$7$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{9}q^{2}+\beta _{1}q^{3}+(-1-\beta _{9})q^{4}+(-\beta _{8}+\cdots)q^{5}+\cdots$
494.2.e.d	$494$	$2$	494.e	247.e	$3$	$22$	$11$	$3.945$		None		$2$	$0$	$-11$	$0$	$-2$	$-5$			$\mathrm{SU}(2)[C_{3}]$
494.2.f.a	$494$	$2$	494.f	19.c	$3$	$2$	$1$	$3.945$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-3$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
494.2.f.b	$494$	$2$	494.f	19.c	$3$	$2$	$1$	$3.945$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
494.2.f.c	$494$	$2$	494.f	19.c	$3$	$2$	$1$	$3.945$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$1$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
494.2.f.d	$494$	$2$	494.f	19.c	$3$	$2$	$1$	$3.945$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$3$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
494.2.f.e	$494$	$2$	494.f	19.c	$3$	$4$	$2$	$3.945$	$\Q(\zeta_{12})$	None		$2$	$0$	$-2$	$0$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{12}^{2}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+(-1+\cdots)q^{4}+\cdots$
494.2.f.f	$494$	$2$	494.f	19.c	$3$	$4$	$2$	$3.945$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		$2$	$0$	$2$	$-2$	$0$	$8$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}-\beta _{1}q^{3}+(-1+\beta _{1})q^{4}-\beta _{2}q^{5}+\cdots$
494.2.f.g	$494$	$2$	494.f	19.c	$3$	$4$	$2$	$3.945$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		$2$	$0$	$2$	$2$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+\beta _{1}q^{3}+(-1+\beta _{1})q^{4}+\beta _{2}q^{5}+\cdots$
494.2.f.h	$494$	$2$	494.f	19.c	$3$	$6$	$3$	$3.945$	6.0.2696112.1	None		$2$	$0$	$-3$	$-2$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{2}+(-\beta _{1}-\beta _{2}-\beta _{4})q^{3}+(-1+\cdots)q^{4}+\cdots$
494.2.f.i	$494$	$2$	494.f	19.c	$3$	$6$	$3$	$3.945$	6.0.591408.1	None		$2$	$0$	$3$	$1$	$2$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}+\beta _{4}q^{3}+(-1+\beta _{3})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
494.2.f.j	$494$	$2$	494.f	19.c	$3$	$8$	$4$	$3.945$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$-4$	$0$	$2$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{3})q^{2}+(-\beta _{1}-\beta _{5})q^{3}+\beta _{3}q^{4}+\cdots$
494.2.g.a	$494$	$2$	494.g	13.c	$3$	$2$	$1$	$3.945$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-2$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
494.2.g.b	$494$	$2$	494.g	13.c	$3$	$6$	$3$	$3.945$	6.0.771147.1	None		$2$	$0$	$-3$	$2$	$4$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{2}+(-\beta _{1}-\beta _{4})q^{3}+(-1-\beta _{4}+\cdots)q^{4}+\cdots$
494.2.g.c	$494$	$2$	494.g	13.c	$3$	$6$	$3$	$3.945$	6.0.34415307.1	None		$2$	$0$	$3$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{4})q^{2}+\beta _{1}q^{3}+\beta _{4}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots$
494.2.g.d	$494$	$2$	494.g	13.c	$3$	$6$	$3$	$3.945$	6.0.34415307.1	None		$2$	$0$	$3$	$0$	$4$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{4})q^{2}+\beta _{1}q^{3}+\beta _{4}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
494.2.g.e	$494$	$2$	494.g	13.c	$3$	$8$	$4$	$3.945$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$4$	$2$	$-2$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}+(1-\beta _{1}+\beta _{5})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
494.2.g.f	$494$	$2$	494.g	13.c	$3$	$12$	$6$	$3.945$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$-6$	$-2$	$4$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{7}q^{2}-\beta _{1}q^{3}+(-1+\beta _{7})q^{4}+(-1+\cdots)q^{5}+\cdots$
494.2.h.a	$494$	$2$	494.h	247.h	$3$	$2$	$1$	$3.945$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-2$	$0$	$-3$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+q^{4}+(-3+3\zeta_{6})q^{5}+(3-3\zeta_{6})q^{7}+\cdots$
494.2.h.b	$494$	$2$	494.h	247.h	$3$	$2$	$1$	$3.945$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-2$	$0$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+q^{4}+(1-\zeta_{6})q^{5}+(-1+\zeta_{6})q^{7}+\cdots$
494.2.h.c	$494$	$2$	494.h	247.h	$3$	$18$	$9$	$3.945$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		$2$	$0$	$-18$	$0$	$4$	$7$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(-\beta _{1}+\beta _{3})q^{3}+q^{4}+(-\beta _{8}+\cdots)q^{5}+\cdots$
494.2.h.d	$494$	$2$	494.h	247.h	$3$	$22$	$11$	$3.945$		None		$2$	$0$	$22$	$0$	$-2$	$-5$			$\mathrm{SU}(2)[C_{3}]$
494.2.i.a	$494$	$2$	494.i	247.i	$4$	$52$	$26$	$3.945$		None		$4$	$0$	$0$	$0$	$0$	$16$			$\mathrm{SU}(2)[C_{4}]$
494.2.m.a	$494$	$2$	494.m	13.e	$6$	$16$	$8$	$3.945$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{12}q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots$
494.2.m.b	$494$	$2$	494.m	13.e	$6$	$28$	$14$	$3.945$		None		$2$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
494.2.n.a	$494$	$2$	494.n	247.q	$6$	$52$	$26$	$3.945$		None		$4$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
494.2.o.a	$494$	$2$	494.o	247.r	$6$	$44$	$22$	$3.945$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
494.2.v.a	$494$	$2$	494.v	247.l	$6$	$44$	$22$	$3.945$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
494.2.w.a	$494$	$2$	494.w	247.w	$9$	$72$	$12$	$3.945$		None		$2$	$0$	$0$	$0$	$0$	$-9$			$\mathrm{SU}(2)[C_{9}]$
494.2.w.b	$494$	$2$	494.w	247.w	$9$	$72$	$12$	$3.945$		None		$2$	$0$	$0$	$0$	$0$	$9$			$\mathrm{SU}(2)[C_{9}]$
494.2.x.a	$494$	$2$	494.x	19.e	$9$	$6$	$1$	$3.945$	$\Q(\zeta_{18})$	None		$2$	$0$	$0$	$6$	$3$	$-3$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(1+\zeta_{18}^{2})q^{3}+\cdots$
494.2.x.b	$494$	$2$	494.x	19.e	$9$	$18$	$3$	$3.945$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		$2$	$0$	$0$	$-3$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+\beta _{8}q^{2}+(-\beta _{4}+\beta _{7})q^{3}+\beta _{9}q^{4}+\cdots$
494.2.x.c	$494$	$2$	494.x	19.e	$9$	$30$	$5$	$3.945$		None		$2$	$0$	$0$	$0$	$3$	$9$			$\mathrm{SU}(2)[C_{9}]$
494.2.x.d	$494$	$2$	494.x	19.e	$9$	$30$	$5$	$3.945$		None		$2$	$0$	$0$	$3$	$-3$	$0$			$\mathrm{SU}(2)[C_{9}]$
494.2.x.e	$494$	$2$	494.x	19.e	$9$	$36$	$6$	$3.945$		None		$2$	$0$	$0$	$0$	$-3$	$0$			$\mathrm{SU}(2)[C_{9}]$
494.2.y.a	$494$	$2$	494.y	247.y	$9$	$72$	$12$	$3.945$		None		$2$	$0$	$0$	$0$	$0$	$-18$			$\mathrm{SU}(2)[C_{9}]$
494.2.y.b	$494$	$2$	494.y	247.y	$9$	$72$	$12$	$3.945$		None		$2$	$0$	$0$	$0$	$0$	$18$			$\mathrm{SU}(2)[C_{9}]$

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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.