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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
286.2.a.a	$286$	$2$	286.a	1.a	$1$	$1$	$1$	$2.284$	$\Q$	None	✓	$1$	$0$	$-1$	$-2$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+3q^{5}+2q^{6}-q^{7}+\cdots$
286.2.a.b	$286$	$2$	286.a	1.a	$1$	$1$	$1$	$2.284$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
286.2.a.c	$286$	$2$	286.a	1.a	$1$	$1$	$1$	$2.284$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$-3$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}-5q^{7}+\cdots$
286.2.a.d	$286$	$2$	286.a	1.a	$1$	$1$	$1$	$2.284$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots$
286.2.a.e	$286$	$2$	286.a	1.a	$1$	$1$	$1$	$2.284$	$\Q$	None	✓	$1$	$0$	$1$	$2$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}+q^{7}+\cdots$
286.2.a.f	$286$	$2$	286.a	1.a	$1$	$1$	$1$	$2.284$	$\Q$	None	✓	$1$	$0$	$1$	$2$	$1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}-3q^{7}+\cdots$
286.2.a.g	$286$	$2$	286.a	1.a	$1$	$3$	$3$	$2.284$	3.3.961.1	None	✓	$1$	$0$	$-3$	$1$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
286.2.b.a	$286$	$2$	286.b	13.b	$2$	$2$	$2$	$2.284$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}+3iq^{5}+iq^{7}-iq^{8}+\cdots$
286.2.b.b	$286$	$2$	286.b	13.b	$2$	$2$	$2$	$2.284$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}-2iq^{5}-4iq^{7}-iq^{8}+\cdots$
286.2.b.c	$286$	$2$	286.b	13.b	$2$	$2$	$2$	$2.284$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+3q^{3}-q^{4}+iq^{5}+3iq^{6}+\cdots$
286.2.b.d	$286$	$2$	286.b	13.b	$2$	$4$	$4$	$2.284$	$\Q(i, \sqrt{17})$	None		$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-1+\beta _{3})q^{3}-q^{4}+\beta _{2}q^{5}+\cdots$
286.2.e.a	$286$	$2$	286.e	13.c	$3$	$2$	$1$	$2.284$	$\Q(\sqrt{-3}) $	None		$2$	$1$	$-1$	$-2$	$-8$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
286.2.e.b	$286$	$2$	286.e	13.c	$3$	$2$	$1$	$2.284$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$-2$	$6$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
286.2.e.c	$286$	$2$	286.e	13.c	$3$	$2$	$1$	$2.284$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$2$	$6$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
286.2.e.d	$286$	$2$	286.e	13.c	$3$	$2$	$1$	$2.284$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$2$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
286.2.e.e	$286$	$2$	286.e	13.c	$3$	$4$	$2$	$2.284$	$\Q(\zeta_{12})$	None		$2$	$0$	$-2$	$2$	$4$	$6$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots$
286.2.e.f	$286$	$2$	286.e	13.c	$3$	$6$	$3$	$2.284$	6.0.591408.1	None		$2$	$0$	$3$	$-4$	$-2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{2}+(-\beta _{1}-\beta _{4})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots$
286.2.e.g	$286$	$2$	286.e	13.c	$3$	$6$	$3$	$2.284$	6.0.954288.1	None		$2$	$0$	$3$	$2$	$-2$	$-2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{3})q^{2}+(1-\beta _{3}+\beta _{5})q^{3}-\beta _{3}q^{4}+\cdots$
286.2.g.a	$286$	$2$	286.g	143.g	$4$	$28$	$14$	$2.284$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
286.2.h.a	$286$	$2$	286.h	11.c	$5$	$4$	$1$	$2.284$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$-4$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\cdots)q^{3}+\cdots$
286.2.h.b	$286$	$2$	286.h	11.c	$5$	$8$	$2$	$2.284$	8.0.159390625.1	None		$2$	$0$	$-2$	$4$	$7$	$8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{3}q^{2}+(-\beta _{1}+\beta _{5}+\beta _{6})q^{3}-\beta _{2}q^{4}+\cdots$
286.2.h.c	$286$	$2$	286.h	11.c	$5$	$12$	$3$	$2.284$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$-3$	$4$	$3$	$-8$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{1}+\beta _{3}+\beta _{9})q^{2}-\beta _{5}q^{3}+\cdots$
286.2.h.d	$286$	$2$	286.h	11.c	$5$	$12$	$3$	$2.284$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$3$	$0$	$3$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{6}q^{2}+(\beta _{4}-\beta _{5}+\beta _{11})q^{3}-\beta _{10}q^{4}+\cdots$
286.2.h.e	$286$	$2$	286.h	11.c	$5$	$12$	$3$	$2.284$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$3$	$4$	$3$	$-6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\beta _{5}-\beta _{6}-\beta _{8})q^{2}+(\beta _{1}-\beta _{7}+\cdots)q^{3}+\cdots$
286.2.j.a	$286$	$2$	286.j	13.e	$6$	$12$	$6$	$2.284$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{6}q^{2}+(\beta _{1}+\beta _{2}+\beta _{4}+2\beta _{5}+2\beta _{7}+\cdots)q^{3}+\cdots$
286.2.j.b	$286$	$2$	286.j	13.e	$6$	$16$	$8$	$2.284$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{11}q^{2}+(-\beta _{2}-\beta _{13})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots$
286.2.n.a	$286$	$2$	286.n	143.n	$10$	$8$	$2$	$2.284$	$\Q(\zeta_{20})$	None		$4$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\zeta_{20}q^{2}+(2-2\zeta_{20}^{2}+2\zeta_{20}^{4}-2\zeta_{20}^{6}+\cdots)q^{3}+\cdots$
286.2.n.b	$286$	$2$	286.n	143.n	$10$	$48$	$12$	$2.284$		None		$4$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
286.2.o.a	$286$	$2$	286.o	143.o	$12$	$56$	$14$	$2.284$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$
286.2.q.a	$286$	$2$	286.q	143.q	$15$	$56$	$7$	$2.284$		None		$4$	$0$	$-7$	$0$	$4$	$-5$			$\mathrm{SU}(2)[C_{15}]$
286.2.q.b	$286$	$2$	286.q	143.q	$15$	$56$	$7$	$2.284$		None		$4$	$0$	$7$	$0$	$-4$	$5$			$\mathrm{SU}(2)[C_{15}]$
286.2.r.a	$286$	$2$	286.r	143.s	$20$	$112$	$14$	$2.284$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{20}]$
286.2.u.a	$286$	$2$	286.u	143.u	$30$	$112$	$14$	$2.284$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{30}]$
286.2.x.a	$286$	$2$	286.x	143.w	$60$	$224$	$14$	$2.284$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{60}]$
286.3.c.a	$286$	$3$	286.c	143.d	$2$	$4$	$4$	$7.793$	$\Q(\sqrt{2}, \sqrt{-161})$	None		$4$	$0$	$0$	$-16$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-4q^{3}+2q^{4}-4\beta _{2}q^{6}+\beta _{2}q^{7}+\cdots$
286.3.c.b	$286$	$3$	286.c	143.d	$2$	$4$	$4$	$7.793$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$20$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+5q^{3}+2q^{4}+9\zeta_{8}^{2}q^{5}+\cdots$
286.3.c.c	$286$	$3$	286.c	143.d	$2$	$20$	$20$	$7.793$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$4$	$0$	$0$	$-4$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{13}q^{2}-\beta _{3}q^{3}+2q^{4}+\beta _{4}q^{5}+\cdots$
286.3.d.a	$286$	$3$	286.d	11.b	$2$	$24$	$24$	$7.793$		None		$2$	$0$	$0$	$-4$	$4$	$0$			$\mathrm{SU}(2)[C_{2}]$
286.3.f.a	$286$	$3$	286.f	13.d	$4$	$24$	$12$	$7.793$		None		$2$	$0$	$24$	$0$	$12$	$-4$			$\mathrm{SU}(2)[C_{4}]$
286.3.f.b	$286$	$3$	286.f	13.d	$4$	$28$	$14$	$7.793$		None		$2$	$0$	$-28$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
286.3.i.a	$286$	$3$	286.i	143.i	$6$	$56$	$28$	$7.793$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
286.3.k.a	$286$	$3$	286.k	143.k	$6$	$56$	$28$	$7.793$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
286.3.l.a	$286$	$3$	286.l	11.d	$10$	$96$	$24$	$7.793$		None		$2$	$0$	$0$	$4$	$-4$	$60$			$\mathrm{SU}(2)[C_{10}]$
286.3.m.a	$286$	$3$	286.m	143.l	$10$	$112$	$28$	$7.793$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
286.3.p.a	$286$	$3$	286.p	13.f	$12$	$40$	$10$	$7.793$		None		$2$	$0$	$-20$	$0$	$-12$	$24$			$\mathrm{SU}(2)[C_{12}]$
286.3.p.b	$286$	$3$	286.p	13.f	$12$	$48$	$12$	$7.793$		None		$2$	$0$	$24$	$0$	$0$	$24$			$\mathrm{SU}(2)[C_{12}]$
286.3.s.a	$286$	$3$	286.s	143.r	$20$	$112$	$14$	$7.793$		None		$4$	$0$	$-28$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{20}]$
286.3.s.b	$286$	$3$	286.s	143.r	$20$	$112$	$14$	$7.793$		None		$4$	$0$	$28$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{20}]$
286.3.t.a	$286$	$3$	286.t	143.t	$30$	$224$	$28$	$7.793$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{30}]$
286.3.v.a	$286$	$3$	286.v	143.v	$30$	$224$	$28$	$7.793$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{30}]$

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Elliptic 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.