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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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Results (36 matches)

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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
667.1.b.a	$667$	$1$	667.b	667.b	$2$	$1$	$1$	$0.333$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-667}) $	$\Q(\sqrt{29}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}+q^{9}-2q^{13}+q^{16}-q^{23}+\cdots$
667.1.b.b	$667$	$1$	667.b	667.b	$2$	$2$	$2$	$0.333$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+(\zeta_{6}+\zeta_{6}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots$
667.1.i.a	$667$	$1$	667.i	667.i	$14$	$6$	$1$	$0.333$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$5$	$-2$	$0$	$0$		$1$		$q+(1+\zeta_{14}^{4})q^{2}+(-\zeta_{14}-\zeta_{14}^{5})q^{3}+\cdots$
667.1.i.b	$667$	$1$	667.i	667.i	$14$	$12$	$2$	$0.333$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-5$	$2$	$0$	$0$		$1$		$q+(-\zeta_{42}+\zeta_{42}^{14})q^{2}+(\zeta_{42}^{16}-\zeta_{42}^{17}+\cdots)q^{3}+\cdots$
667.1.k.a	$667$	$1$	667.k	667.k	$14$	$6$	$1$	$0.333$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-7$	$0$	$0$	$0$		$1$		$q+(-1+\zeta_{14}^{4})q^{2}+(-\zeta_{14}+\zeta_{14}^{5}+\cdots)q^{3}+\cdots$
667.1.k.b	$667$	$1$	667.k	667.k	$14$	$12$	$2$	$0.333$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$7$	$0$	$0$	$0$		$1$		$q+(\zeta_{42}^{7}+\zeta_{42}^{8})q^{2}+(\zeta_{42}^{2}-\zeta_{42}^{10}+\cdots)q^{3}+\cdots$
667.2.a.a	$667$	$2$	667.a	1.a	$1$	$10$	$10$	$5.326$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-3$	$-9$	$-10$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots$
667.2.a.b	$667$	$2$	667.a	1.a	$1$	$12$	$12$	$5.326$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-3$	$-3$	$-16$	$-7$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{5}q^{3}+(1-\beta _{4}-\beta _{6}+\beta _{8}+\cdots)q^{4}+\cdots$
667.2.a.c	$667$	$2$	667.a	1.a	$1$	$13$	$13$	$5.326$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$4$	$3$	$16$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{12}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
667.2.a.d	$667$	$2$	667.a	1.a	$1$	$16$	$16$	$5.326$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$5$	$16$	$1$	$-$	$2^{6}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
667.2.c.a	$667$	$2$	667.c	29.b	$2$	$24$	$24$	$5.326$		$_{}$	None	None		$2$	$0$	$0$	$0$	$6$	$-14$			$\mathrm{SU}(2)[C_{2}]$
667.2.c.b	$667$	$2$	667.c	29.b	$2$	$30$	$30$	$5.326$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$6$			$\mathrm{SU}(2)[C_{2}]$
667.2.f.a	$667$	$2$	667.f	667.f	$4$	$12$	$6$	$5.326$	12.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{4}]$	$q+(\beta _{1}-\beta _{9}-\beta _{10})q^{2}+(-\beta _{3}+\beta _{8}+\cdots)q^{3}+\cdots$
667.2.f.b	$667$	$2$	667.f	667.f	$4$	$104$	$52$	$5.326$		$_{}$	None	None		$4$	$0$	$-8$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
667.2.g.a	$667$	$2$	667.g	29.d	$7$	$6$	$1$	$5.326$	$\Q(\zeta_{14})$	$_{}$	None	None		$2$	$0$	$-2$	$1$	$2$	$-13$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-1+\zeta_{14}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots$
667.2.g.b	$667$	$2$	667.g	29.d	$7$	$144$	$24$	$5.326$		$_{}$	None	None		$2$	$0$	$1$	$-1$	$-2$	$19$			$\mathrm{SU}(2)[C_{7}]$
667.2.g.c	$667$	$2$	667.g	29.d	$7$	$186$	$31$	$5.326$		$_{}$	None	None		$2$	$0$	$-1$	$0$	$-8$	$-14$			$\mathrm{SU}(2)[C_{7}]$
667.2.h.a	$667$	$2$	667.h	23.c	$11$	$280$	$28$	$5.326$		$_{}$	None	None		$2$	$0$	$0$	$-2$	$-8$	$-10$			$\mathrm{SU}(2)[C_{11}]$
667.2.h.b	$667$	$2$	667.h	23.c	$11$	$280$	$28$	$5.326$		$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$6$			$\mathrm{SU}(2)[C_{11}]$
667.2.j.a	$667$	$2$	667.j	29.e	$14$	$144$	$24$	$5.326$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-6$	$14$			$\mathrm{SU}(2)[C_{14}]$
667.2.j.b	$667$	$2$	667.j	29.e	$14$	$180$	$30$	$5.326$		$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$-6$			$\mathrm{SU}(2)[C_{14}]$
667.2.m.a	$667$	$2$	667.m	667.m	$22$	$580$	$58$	$5.326$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-14$	$-22$			$\mathrm{SU}(2)[C_{22}]$
667.2.o.a	$667$	$2$	667.o	667.o	$28$	$72$	$6$	$5.326$		$_{}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{28}]$
667.2.o.b	$667$	$2$	667.o	667.o	$28$	$624$	$52$	$5.326$		$_{}$	None	None		$4$	$0$	$-20$	$-24$	$0$	$0$			$\mathrm{SU}(2)[C_{28}]$
667.2.q.a	$667$	$2$	667.q	667.q	$44$	$1160$	$58$	$5.326$		$_{}$	None	None		$4$	$0$	$-14$	$-18$	$0$	$-44$			$\mathrm{SU}(2)[C_{44}]$
667.2.s.a	$667$	$2$	667.s	667.s	$77$	$3480$	$58$	$5.326$		$_{}$	None	None		$4$	$0$	$-49$	$-45$	$-49$	$-49$			$\mathrm{SU}(2)[C_{77}]$
667.2.u.a	$667$	$2$	667.u	667.u	$154$	$3480$	$58$	$5.326$		$_{}$	None	None		$4$	$0$	$-63$	$-63$	$-49$	$-41$			$\mathrm{SU}(2)[C_{154}]$
667.2.x.a	$667$	$2$	667.x	667.x	$308$	$6960$	$58$	$5.326$		$_{}$	None	None		$4$	$0$	$-112$	$-108$	$-154$	$-110$			$\mathrm{SU}(2)[C_{308}]$
667.4.a.a	$667$	$4$	667.a	1.a	$1$	$35$	$35$	$39.354$		$_{}$	None	None	✓	$1$	$1$	$-6$	$-22$	$-80$	$-38$	$-$		$\mathrm{SU}(2)$
667.4.a.b	$667$	$4$	667.a	1.a	$1$	$38$	$38$	$39.354$		$_{}$	None	None	✓	$1$	$1$	$-8$	$-16$	$-80$	$-38$	$-$		$\mathrm{SU}(2)$
667.4.a.c	$667$	$4$	667.a	1.a	$1$	$39$	$39$	$39.354$		$_{}$	None	None	✓	$1$	$0$	$6$	$2$	$80$	$18$	$+$		$\mathrm{SU}(2)$
667.4.a.d	$667$	$4$	667.a	1.a	$1$	$42$	$42$	$39.354$		$_{}$	None	None	✓	$1$	$0$	$12$	$32$	$80$	$18$	$+$		$\mathrm{SU}(2)$
667.6.a.a	$667$	$6$	667.a	1.a	$1$	$61$	$61$	$106.976$		$_{}$	None	None	✓	$1$	$1$	$-24$	$-97$	$-400$	$-243$	$+$		$\mathrm{SU}(2)$
667.6.a.b	$667$	$6$	667.a	1.a	$1$	$64$	$64$	$106.976$		$_{}$	None	None	✓	$1$	$1$	$-12$	$-7$	$-400$	$-243$	$+$		$\mathrm{SU}(2)$
667.6.a.c	$667$	$6$	667.a	1.a	$1$	$65$	$65$	$106.976$		$_{}$	None	None	✓	$1$	$0$	$16$	$47$	$400$	$149$	$-$		$\mathrm{SU}(2)$
667.6.a.d	$667$	$6$	667.a	1.a	$1$	$68$	$68$	$106.976$		$_{}$	None	None	✓	$1$	$0$	$12$	$65$	$400$	$149$	$-$		$\mathrm{SU}(2)$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
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Abelian varieties over $\F_{q}$

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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.