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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 (47 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
1045.1.k.a	$1045$	$1$	1045.k	1045.k	$4$	$2$	$1$	$0.522$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{209}) $		$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q+(-1-i)q^{2}+iq^{4}-iq^{5}-q^{8}+\cdots$
1045.1.k.b	$1045$	$1$	1045.k	1045.k	$4$	$2$	$1$	$0.522$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$-2$		$1$		$q-iq^{4}+q^{5}+(-1+i)q^{7}-iq^{9}+\cdots$
1045.1.k.c	$1045$	$1$	1045.k	1045.k	$4$	$2$	$1$	$0.522$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$2$		$1$		$q-iq^{4}+q^{5}+(1-i)q^{7}-iq^{9}+iq^{11}+\cdots$
1045.1.k.d	$1045$	$1$	1045.k	1045.k	$4$	$2$	$1$	$0.522$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{209}) $		$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+(1+i)q^{2}+iq^{4}-iq^{5}+q^{8}-iq^{9}+\cdots$
1045.1.w.a	$1045$	$1$	1045.w	1045.w	$10$	$4$	$1$	$0.522$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-95}) $	None		$4$	$0$	$-2$	$-2$	$-1$	$0$		$1$		$q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
1045.1.w.b	$1045$	$1$	1045.w	1045.w	$10$	$4$	$1$	$0.522$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-1$	$-5$		$1$		$q+\zeta_{10}q^{4}-\zeta_{10}q^{5}+(-1+\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
1045.1.w.c	$1045$	$1$	1045.w	1045.w	$10$	$4$	$1$	$0.522$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-1$	$5$		$1$		$q+\zeta_{10}q^{4}-\zeta_{10}^{3}q^{5}+(1-\zeta_{10}^{2})q^{7}+\cdots$
1045.1.w.d	$1045$	$1$	1045.w	1045.w	$10$	$4$	$1$	$0.522$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-95}) $	None		$4$	$0$	$2$	$2$	$-1$	$0$		$1$		$q+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{2}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
1045.1.w.e	$1045$	$1$	1045.w	1045.w	$10$	$8$	$2$	$0.522$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$-2$	$0$		$5$		$q+(-\zeta_{20}^{3}-\zeta_{20}^{9})q^{2}+(\zeta_{20}^{7}+\zeta_{20}^{9}+\cdots)q^{3}+\cdots$
1045.1.w.f	$1045$	$1$	1045.w	1045.w	$10$	$16$	$4$	$0.522$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$4$	$0$		$1$		$q+(\zeta_{40}+\zeta_{40}^{7})q^{2}+(\zeta_{40}^{11}+\zeta_{40}^{13}+\cdots)q^{3}+\cdots$
1045.1.br.a	$1045$	$1$	1045.br	1045.ar	$20$	$8$	$1$	$0.522$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-8$		$1$		$q-\zeta_{20}^{3}q^{4}+\zeta_{20}^{4}q^{5}+(-1-\zeta_{20}+\cdots)q^{7}+\cdots$
1045.1.br.b	$1045$	$1$	1045.br	1045.ar	$20$	$8$	$1$	$0.522$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-2$		$1$		$q-\zeta_{20}^{3}q^{4}+\zeta_{20}^{8}q^{5}+(\zeta_{20}^{5}-\zeta_{20}^{6}+\cdots)q^{7}+\cdots$
1045.2.a.a	$1045$	$2$	1045.a	1.a	$1$	$1$	$1$	$8.344$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-2$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}-q^{4}-q^{5}+2q^{6}-2q^{7}+\cdots$
1045.2.a.b	$1045$	$2$	1045.a	1.a	$1$	$1$	$1$	$8.344$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}-3q^{8}-3q^{9}+q^{10}+\cdots$
1045.2.a.c	$1045$	$2$	1045.a	1.a	$1$	$2$	$2$	$8.344$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$4$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+2q^{3}+(1+2\beta )q^{4}+q^{5}+\cdots$
1045.2.a.d	$1045$	$2$	1045.a	1.a	$1$	$5$	$5$	$8.344$	$\Q(\zeta_{22})^+$	$_{}$	None	None	✓	$1$	$1$	$-3$	$-7$	$5$	$-11$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}-\beta _{4})q^{2}+(-2-\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots$
1045.2.a.e	$1045$	$2$	1045.a	1.a	$1$	$5$	$5$	$8.344$	5.5.36497.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-3$	$-5$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+(-1+\beta _{1})q^{3}+\beta _{3}q^{4}-q^{5}+\cdots$
1045.2.a.f	$1045$	$2$	1045.a	1.a	$1$	$6$	$6$	$8.344$	6.6.7281497.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$-1$	$-6$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{2}+\beta _{3}q^{3}+(\beta _{4}+\beta _{5})q^{4}-q^{5}+\cdots$
1045.2.a.g	$1045$	$2$	1045.a	1.a	$1$	$6$	$6$	$8.344$	6.6.131947641.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$6$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(2+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
1045.2.a.h	$1045$	$2$	1045.a	1.a	$1$	$7$	$7$	$8.344$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$3$	$-7$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
1045.2.a.i	$1045$	$2$	1045.a	1.a	$1$	$8$	$8$	$8.344$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-6$	$-7$	$8$	$-11$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-1-\beta _{6})q^{3}+(2+\cdots)q^{4}+\cdots$
1045.2.a.j	$1045$	$2$	1045.a	1.a	$1$	$9$	$9$	$8.344$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$3$	$-9$	$-9$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(1-\beta _{1}-\beta _{8})q^{4}+\cdots$
1045.2.a.k	$1045$	$2$	1045.a	1.a	$1$	$9$	$9$	$8.344$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$3$	$9$	$13$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
1045.2.b.a	$1045$	$2$	1045.b	5.b	$2$	$4$	$4$	$8.344$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}q^{2}+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(-1-\zeta_{8}^{3})q^{4}+\cdots$
1045.2.b.b	$1045$	$2$	1045.b	5.b	$2$	$16$	$16$	$8.344$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$3$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{11}q^{3}+\beta _{2}q^{4}+(\beta _{3}+\beta _{13}+\cdots)q^{5}+\cdots$
1045.2.b.c	$1045$	$2$	1045.b	5.b	$2$	$20$	$20$	$8.344$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{7}q^{3}+(-1+\beta _{2})q^{4}-\beta _{11}q^{5}+\cdots$
1045.2.b.d	$1045$	$2$	1045.b	5.b	$2$	$22$	$22$	$8.344$		$_{}$	None	None		$2$	$0$	$0$	$0$	$7$	$0$			$\mathrm{SU}(2)[C_{2}]$
1045.2.b.e	$1045$	$2$	1045.b	5.b	$2$	$30$	$30$	$8.344$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1045.2.f.a	$1045$	$2$	1045.f	209.d	$2$	$40$	$40$	$8.344$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-40$	$0$			$\mathrm{SU}(2)[C_{2}]$
1045.2.f.b	$1045$	$2$	1045.f	209.d	$2$	$40$	$40$	$8.344$		$_{}$	None	None		$4$	$0$	$0$	$0$	$40$	$0$			$\mathrm{SU}(2)[C_{2}]$
1045.4.a.a	$1045$	$4$	1045.a	1.a	$1$	$1$	$1$	$61.657$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-5$	$-1$	$-5$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-5q^{2}-q^{3}+17q^{4}-5q^{5}+5q^{6}+\cdots$
1045.4.a.b	$1045$	$4$	1045.a	1.a	$1$	$20$	$20$	$61.657$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-12$	$-21$	$100$	$-131$	$-$	$2^{3}\cdot 7$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-1+\beta _{5})q^{3}+(4+\cdots)q^{4}+\cdots$
1045.4.a.c	$1045$	$4$	1045.a	1.a	$1$	$20$	$20$	$61.657$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-8$	$-100$	$49$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(3+\beta _{2})q^{4}-5q^{5}+\cdots$
1045.4.a.d	$1045$	$4$	1045.a	1.a	$1$	$22$	$22$	$61.657$		$_{}$	None	None	✓	$1$	$1$	$-4$	$-21$	$110$	$-41$	$-$		$\mathrm{SU}(2)$
1045.4.a.e	$1045$	$4$	1045.a	1.a	$1$	$22$	$22$	$61.657$		$_{}$	None	None	✓	$1$	$0$	$12$	$21$	$110$	$93$	$+$		$\mathrm{SU}(2)$
1045.4.a.f	$1045$	$4$	1045.a	1.a	$1$	$23$	$23$	$61.657$		$_{}$	None	None	✓	$1$	$1$	$-2$	$-9$	$-115$	$13$	$-$		$\mathrm{SU}(2)$
1045.4.a.g	$1045$	$4$	1045.a	1.a	$1$	$23$	$23$	$61.657$		$_{}$	None	None	✓	$1$	$0$	$6$	$9$	$-115$	$-37$	$+$		$\mathrm{SU}(2)$
1045.4.a.h	$1045$	$4$	1045.a	1.a	$1$	$24$	$24$	$61.657$		$_{}$	None	None	✓	$1$	$0$	$4$	$21$	$120$	$71$	$+$		$\mathrm{SU}(2)$
1045.4.a.i	$1045$	$4$	1045.a	1.a	$1$	$25$	$25$	$61.657$		$_{}$	None	None	✓	$1$	$0$	$2$	$9$	$-125$	$-15$	$+$		$\mathrm{SU}(2)$
1045.6.a.a	$1045$	$6$	1045.a	1.a	$1$	$35$	$35$	$167.601$		$_{}$	None	None	✓	$1$	$1$	$-4$	$-27$	$-875$	$117$	$+$		$\mathrm{SU}(2)$
1045.6.a.b	$1045$	$6$	1045.a	1.a	$1$	$36$	$36$	$167.601$		$_{}$	None	None	✓	$1$	$1$	$-8$	$-63$	$900$	$-509$	$+$		$\mathrm{SU}(2)$
1045.6.a.c	$1045$	$6$	1045.a	1.a	$1$	$37$	$37$	$167.601$		$_{}$	None	None	✓	$1$	$1$	$-12$	$-27$	$-925$	$337$	$+$		$\mathrm{SU}(2)$
1045.6.a.d	$1045$	$6$	1045.a	1.a	$1$	$37$	$37$	$167.601$		$_{}$	None	None	✓	$1$	$0$	$4$	$27$	$-925$	$-79$	$-$		$\mathrm{SU}(2)$
1045.6.a.e	$1045$	$6$	1045.a	1.a	$1$	$38$	$38$	$167.601$		$_{}$	None	None	✓	$1$	$1$	$-24$	$-63$	$950$	$-729$	$+$		$\mathrm{SU}(2)$
1045.6.a.f	$1045$	$6$	1045.a	1.a	$1$	$38$	$38$	$167.601$		$_{}$	None	None	✓	$1$	$0$	$8$	$63$	$950$	$275$	$-$		$\mathrm{SU}(2)$
1045.6.a.g	$1045$	$6$	1045.a	1.a	$1$	$39$	$39$	$167.601$		$_{}$	None	None	✓	$1$	$0$	$12$	$27$	$-975$	$-251$	$-$		$\mathrm{SU}(2)$
1045.6.a.h	$1045$	$6$	1045.a	1.a	$1$	$40$	$40$	$167.601$		$_{}$	None	None	✓	$1$	$0$	$24$	$63$	$1000$	$839$	$-$		$\mathrm{SU}(2)$

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Hilbert	Bianchi

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.