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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
170.2.a.a	$170$	$2$	170.a	1.a	$1$	$1$	$1$	$1.357$	$\Q$	None	✓	$1$	$0$	$-1$	$-2$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}-q^{5}+2q^{6}+2q^{7}+\cdots$
170.2.a.b	$170$	$2$	170.a	1.a	$1$	$1$	$1$	$1.357$	$\Q$	None	✓	$1$	$1$	$-1$	$-2$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots$
170.2.a.c	$170$	$2$	170.a	1.a	$1$	$1$	$1$	$1.357$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots$
170.2.a.d	$170$	$2$	170.a	1.a	$1$	$1$	$1$	$1.357$	$\Q$	None	✓	$1$	$0$	$-1$	$3$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-q^{5}-3q^{6}+2q^{7}+\cdots$
170.2.a.e	$170$	$2$	170.a	1.a	$1$	$1$	$1$	$1.357$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots$
170.2.a.f	$170$	$2$	170.a	1.a	$1$	$2$	$2$	$1.357$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$2$	$-1$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+2\beta q^{7}+\cdots$
170.2.b.a	$170$	$2$	170.b	17.b	$2$	$2$	$2$	$1.357$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+iq^{3}+q^{4}+iq^{5}-iq^{6}-q^{8}+\cdots$
170.2.b.b	$170$	$2$	170.b	17.b	$2$	$2$	$2$	$1.357$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+3iq^{3}+q^{4}+iq^{5}+3iq^{6}+\cdots$
170.2.b.c	$170$	$2$	170.b	17.b	$2$	$2$	$2$	$1.357$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+iq^{5}+2iq^{7}+q^{8}+3q^{9}+\cdots$
170.2.c.a	$170$	$2$	170.c	5.b	$2$	$2$	$2$	$1.357$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+iq^{3}-q^{4}+(1+2i)q^{5}-q^{6}+\cdots$
170.2.c.b	$170$	$2$	170.c	5.b	$2$	$6$	$6$	$1.357$	6.0.5161984.1	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{5})q^{3}-q^{4}+\cdots$
170.2.d.a	$170$	$2$	170.d	85.c	$2$	$2$	$2$	$1.357$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$-2$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{3}-q^{4}+(-2+i)q^{5}-iq^{6}+\cdots$
170.2.d.b	$170$	$2$	170.d	85.c	$2$	$2$	$2$	$1.357$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$2$	$4$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{3}-q^{4}+(2-i)q^{5}+iq^{6}+\cdots$
170.2.d.c	$170$	$2$	170.d	85.c	$2$	$4$	$4$	$1.357$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{2}+(-2\zeta_{8}+2\zeta_{8}^{3})q^{3}-q^{4}+\cdots$
170.2.g.a	$170$	$2$	170.g	85.j	$4$	$2$	$1$	$1.357$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$2$	$2$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}+(1-i)q^{3}+q^{4}+(1-2i)q^{5}+\cdots$
170.2.g.b	$170$	$2$	170.g	85.j	$4$	$2$	$1$	$1.357$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$2$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}+(1-i)q^{3}+q^{4}+(1+2i)q^{5}+\cdots$
170.2.g.c	$170$	$2$	170.g	85.j	$4$	$2$	$1$	$1.357$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$-2$	$-4$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+(-1+i)q^{3}+q^{4}+(-2+i)q^{5}+\cdots$
170.2.g.d	$170$	$2$	170.g	85.j	$4$	$2$	$1$	$1.357$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$-2$	$4$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+(-1+i)q^{3}+q^{4}+(2+i)q^{5}+\cdots$
170.2.g.e	$170$	$2$	170.g	85.j	$4$	$4$	$2$	$1.357$	$\Q(\zeta_{8})$	None		$2$	$0$	$-4$	$-4$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+q^{4}+\cdots$
170.2.g.f	$170$	$2$	170.g	85.j	$4$	$4$	$2$	$1.357$	$\Q(\zeta_{8})$	None		$2$	$0$	$4$	$4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+q^{4}+(\zeta_{8}+\cdots)q^{5}+\cdots$
170.2.h.a	$170$	$2$	170.h	17.c	$4$	$4$	$2$	$1.357$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$4$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{2}q^{2}+(1+\zeta_{8}+\zeta_{8}^{2})q^{3}-q^{4}+\cdots$
170.2.h.b	$170$	$2$	170.h	17.c	$4$	$8$	$4$	$1.357$	8.0.$\cdots$.1	None		$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{2}-\beta _{7}q^{3}-q^{4}+\beta _{4}q^{5}-\beta _{6}q^{6}+\cdots$
170.2.k.a	$170$	$2$	170.k	17.d	$8$	$8$	$2$	$1.357$	$\Q(\zeta_{16})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+\zeta_{16}^{2}q^{2}+(\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{3}+\cdots)q^{3}+\cdots$
170.2.k.b	$170$	$2$	170.k	17.d	$8$	$16$	$4$	$1.357$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+\beta _{9}q^{2}+(-\beta _{6}+\beta _{15})q^{3}-\beta _{3}q^{4}+\cdots$
170.2.n.a	$170$	$2$	170.n	85.m	$8$	$20$	$5$	$1.357$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$0$	$-4$	$0$		$2$	$\mathrm{SU}(2)[C_{8}]$	$q+\beta _{7}q^{2}-\beta _{6}q^{3}-\beta _{10}q^{4}+\beta _{14}q^{5}+\cdots$
170.2.n.b	$170$	$2$	170.n	85.m	$8$	$20$	$5$	$1.357$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$0$	$-4$	$0$		$2$	$\mathrm{SU}(2)[C_{8}]$	$q+\beta _{8}q^{2}+\beta _{5}q^{3}+\beta _{10}q^{4}-\beta _{16}q^{5}+\cdots$
170.2.o.a	$170$	$2$	170.o	85.o	$16$	$32$	$4$	$1.357$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
170.2.o.b	$170$	$2$	170.o	85.o	$16$	$40$	$5$	$1.357$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
170.2.r.a	$170$	$2$	170.r	85.r	$16$	$32$	$4$	$1.357$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
170.2.r.b	$170$	$2$	170.r	85.r	$16$	$40$	$5$	$1.357$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
170.3.e.a	$170$	$3$	170.e	85.f	$4$	$2$	$1$	$4.632$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-i)q^{2}+4iq^{3}+2iq^{4}-5iq^{5}+\cdots$
170.3.e.b	$170$	$3$	170.e	85.f	$4$	$16$	$8$	$4.632$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$16$	$0$	$-2$	$0$		$2\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\beta _{5})q^{2}-\beta _{1}q^{3}-2\beta _{5}q^{4}-\beta _{12}q^{5}+\cdots$
170.3.e.c	$170$	$3$	170.e	85.f	$4$	$18$	$9$	$4.632$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		$2$	$0$	$-18$	$0$	$8$	$0$		$2^{2}\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{4})q^{2}-\beta _{1}q^{3}+2\beta _{4}q^{4}+\cdots$
170.3.f.a	$170$	$3$	170.f	85.g	$4$	$16$	$8$	$4.632$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$-16$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{3})q^{2}+\beta _{1}q^{3}-2\beta _{3}q^{4}+\cdots$
170.3.f.b	$170$	$3$	170.f	85.g	$4$	$20$	$10$	$4.632$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$4$	$0$	$20$	$0$	$0$	$0$		$2^{3}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{5})q^{2}+\beta _{8}q^{3}+2\beta _{5}q^{4}+\beta _{9}q^{5}+\cdots$
170.3.i.a	$170$	$3$	170.i	5.c	$4$	$16$	$8$	$4.632$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-16$	$8$	$-8$	$4$		$2\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{4})q^{2}+(1-\beta _{1}-\beta _{4})q^{3}+\cdots$
170.3.i.b	$170$	$3$	170.i	5.c	$4$	$16$	$8$	$4.632$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$16$	$0$	$8$	$12$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{3})q^{2}-\beta _{1}q^{3}+2\beta _{3}q^{4}-\beta _{10}q^{5}+\cdots$
170.3.j.a	$170$	$3$	170.j	85.i	$4$	$2$	$1$	$4.632$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$8$	$-10$	$16$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-i)q^{2}+4q^{3}-2iq^{4}-5q^{5}+\cdots$
170.3.j.b	$170$	$3$	170.j	85.i	$4$	$16$	$8$	$4.632$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$-16$	$0$	$2$	$-12$		$2\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{5})q^{2}+\beta _{3}q^{3}+2\beta _{5}q^{4}+\cdots$
170.3.j.c	$170$	$3$	170.j	85.i	$4$	$18$	$9$	$4.632$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		$2$	$0$	$18$	$-8$	$18$	$-28$		$2^{2}\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{4})q^{2}-\beta _{3}q^{3}+2\beta _{4}q^{4}+(1+\cdots)q^{5}+\cdots$
170.3.l.a	$170$	$3$	170.l	85.k	$8$	$36$	$9$	$4.632$		None		$2$	$0$	$0$	$0$	$-4$	$-12$			$\mathrm{SU}(2)[C_{8}]$
170.3.l.b	$170$	$3$	170.l	85.k	$8$	$36$	$9$	$4.632$		None		$2$	$0$	$0$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{8}]$
170.3.m.a	$170$	$3$	170.m	85.n	$8$	$36$	$9$	$4.632$		None		$2$	$0$	$0$	$0$	$-8$	$12$			$\mathrm{SU}(2)[C_{8}]$
170.3.m.b	$170$	$3$	170.m	85.n	$8$	$36$	$9$	$4.632$		None		$2$	$0$	$0$	$0$	$-4$	$12$			$\mathrm{SU}(2)[C_{8}]$
170.3.p.a	$170$	$3$	170.p	17.e	$16$	$48$	$6$	$4.632$		None		$2$	$0$	$0$	$-16$	$0$	$-16$			$\mathrm{SU}(2)[C_{16}]$
170.3.p.b	$170$	$3$	170.p	17.e	$16$	$48$	$6$	$4.632$		None		$2$	$0$	$0$	$16$	$0$	$16$			$\mathrm{SU}(2)[C_{16}]$
170.3.q.a	$170$	$3$	170.q	85.p	$16$	$72$	$9$	$4.632$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
170.3.q.b	$170$	$3$	170.q	85.p	$16$	$72$	$9$	$4.632$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
170.4.a.a	$170$	$4$	170.a	1.a	$1$	$1$	$1$	$10.030$	$\Q$	None	✓	$1$	$1$	$-2$	$4$	$-5$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots$
170.4.a.b	$170$	$4$	170.a	1.a	$1$	$1$	$1$	$10.030$	$\Q$	None	✓	$1$	$0$	$2$	$7$	$5$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+7q^{3}+4q^{4}+5q^{5}+14q^{6}+\cdots$

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Elliptic curves over $\Q$
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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.