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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
2805.1.ba.a	$2805$	$1$	2805.ba	2805.aa	$4$	$4$	$2$	$1.400$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-51}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}-\zeta_{8}^{2}q^{9}+\cdots$
2805.1.ba.b	$2805$	$1$	2805.ba	2805.aa	$4$	$4$	$2$	$1.400$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-51}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}-\zeta_{8}^{2}q^{9}+\cdots$
2805.1.cg.a	$2805$	$1$	2805.cg	2805.bg	$10$	$4$	$1$	$1.400$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-255}) $	None		$4$	$0$	$-3$	$-1$	$1$	$-2$		$1$		$q+(-1+\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
2805.1.cg.b	$2805$	$1$	2805.cg	2805.bg	$10$	$4$	$1$	$1.400$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-255}) $	None		$4$	$0$	$-3$	$1$	$-1$	$2$		$1$		$q+(-1+\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
2805.1.cg.c	$2805$	$1$	2805.cg	2805.bg	$10$	$4$	$1$	$1.400$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-255}) $	None		$4$	$0$	$3$	$-1$	$-1$	$-2$		$1$		$q+(1-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
2805.1.cg.d	$2805$	$1$	2805.cg	2805.bg	$10$	$4$	$1$	$1.400$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-255}) $	None		$4$	$0$	$3$	$1$	$1$	$2$		$1$		$q+(1-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
2805.1.cg.e	$2805$	$1$	2805.cg	2805.bg	$10$	$8$	$2$	$1.400$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-255}) $	None		$4$	$0$	$-3$	$-2$	$-2$	$2$		$1$		$q+(\zeta_{30}^{4}-\zeta_{30}^{5})q^{2}+\zeta_{30}^{6}q^{3}+(\zeta_{30}^{8}+\cdots)q^{4}+\cdots$
2805.1.cg.f	$2805$	$1$	2805.cg	2805.bg	$10$	$8$	$2$	$1.400$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-255}) $	None		$4$	$0$	$-3$	$2$	$2$	$-2$		$1$		$q+(\zeta_{30}^{4}-\zeta_{30}^{5})q^{2}-\zeta_{30}^{6}q^{3}+(\zeta_{30}^{8}+\cdots)q^{4}+\cdots$
2805.1.cg.g	$2805$	$1$	2805.cg	2805.bg	$10$	$8$	$2$	$1.400$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-51}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{20}^{9}q^{3}+\zeta_{20}^{6}q^{4}+\zeta_{20}^{5}q^{5}+\cdots$
2805.1.cg.h	$2805$	$1$	2805.cg	2805.bg	$10$	$8$	$2$	$1.400$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-51}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{20}^{9}q^{3}+\zeta_{20}^{6}q^{4}+\zeta_{20}^{9}q^{5}+\cdots$
2805.1.cg.i	$2805$	$1$	2805.cg	2805.bg	$10$	$8$	$2$	$1.400$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-255}) $	None		$4$	$0$	$3$	$-2$	$2$	$2$		$1$		$q+(-\zeta_{30}^{4}+\zeta_{30}^{5})q^{2}+\zeta_{30}^{6}q^{3}+\cdots$
2805.1.cg.j	$2805$	$1$	2805.cg	2805.bg	$10$	$8$	$2$	$1.400$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-255}) $	None		$4$	$0$	$3$	$2$	$-2$	$-2$		$1$		$q+(-\zeta_{30}^{10}-\zeta_{30}^{14})q^{2}-\zeta_{30}^{6}q^{3}+\cdots$
2805.1.dx.a	$2805$	$1$	2805.dx	2805.cx	$20$	$16$	$2$	$1.400$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-51}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{40}^{3}q^{3}-\zeta_{40}^{2}q^{4}-\zeta_{40}^{15}q^{5}+\cdots$
2805.1.dx.b	$2805$	$1$	2805.dx	2805.cx	$20$	$16$	$2$	$1.400$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-51}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{40}^{3}q^{3}-\zeta_{40}^{2}q^{4}-\zeta_{40}^{3}q^{5}+\cdots$
2805.2.a.a	$2805$	$2$	2805.a	1.a	$1$	$1$	$1$	$22.398$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}+3q^{8}+\cdots$
2805.2.a.b	$2805$	$2$	2805.a	1.a	$1$	$1$	$1$	$22.398$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}-q^{7}+q^{9}-q^{11}+\cdots$
2805.2.a.c	$2805$	$2$	2805.a	1.a	$1$	$1$	$1$	$22.398$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$-1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}+4q^{7}+\cdots$
2805.2.a.d	$2805$	$2$	2805.a	1.a	$1$	$1$	$1$	$22.398$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots$
2805.2.a.e	$2805$	$2$	2805.a	1.a	$1$	$1$	$1$	$22.398$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-3q^{8}+\cdots$
2805.2.a.f	$2805$	$2$	2805.a	1.a	$1$	$2$	$2$	$22.398$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$-2$	$-2$	$-2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots$
2805.2.a.g	$2805$	$2$	2805.a	1.a	$1$	$4$	$4$	$22.398$	4.4.1957.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$4$	$4$	$-11$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+q^{3}+(1-\beta _{1}-\beta _{3})q^{4}+\cdots$
2805.2.a.h	$2805$	$2$	2805.a	1.a	$1$	$4$	$4$	$22.398$	4.4.725.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-4$	$-4$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(-1+\beta _{1}+\beta _{2})q^{4}+\cdots$
2805.2.a.i	$2805$	$2$	2805.a	1.a	$1$	$4$	$4$	$22.398$	4.4.725.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$4$	$4$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(-1+\beta _{1}+\beta _{2})q^{4}+\cdots$
2805.2.a.j	$2805$	$2$	2805.a	1.a	$1$	$4$	$4$	$22.398$	4.4.12357.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$4$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
2805.2.a.k	$2805$	$2$	2805.a	1.a	$1$	$5$	$5$	$22.398$	5.5.81589.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$5$	$-5$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2}-\beta _{3})q^{2}+q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
2805.2.a.l	$2805$	$2$	2805.a	1.a	$1$	$5$	$5$	$22.398$	5.5.81509.1	$_{}$	None	None	✓	$1$	$1$	$2$	$-5$	$-5$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}-q^{3}+(-\beta _{3}-\beta _{4})q^{4}-q^{5}+\cdots$
2805.2.a.m	$2805$	$2$	2805.a	1.a	$1$	$6$	$6$	$22.398$	6.6.225947669.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-6$	$6$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
2805.2.a.n	$2805$	$2$	2805.a	1.a	$1$	$6$	$6$	$22.398$	6.6.94698456.1	$_{}$	None	None	✓	$1$	$0$	$1$	$6$	$-6$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(\beta _{2}+\beta _{4})q^{4}-q^{5}+\cdots$
2805.2.a.o	$2805$	$2$	2805.a	1.a	$1$	$7$	$7$	$22.398$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-3$	$-7$	$7$	$-10$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
2805.2.a.p	$2805$	$2$	2805.a	1.a	$1$	$7$	$7$	$22.398$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$-7$	$7$	$11$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{4}+\beta _{5})q^{4}+q^{5}+\cdots$
2805.2.a.q	$2805$	$2$	2805.a	1.a	$1$	$7$	$7$	$22.398$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$2$	$7$	$-7$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
2805.2.a.r	$2805$	$2$	2805.a	1.a	$1$	$7$	$7$	$22.398$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$-7$	$-7$	$-6$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
2805.2.a.s	$2805$	$2$	2805.a	1.a	$1$	$7$	$7$	$22.398$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$7$	$7$	$10$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
2805.2.a.t	$2805$	$2$	2805.a	1.a	$1$	$8$	$8$	$22.398$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-2$	$-8$	$-8$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
2805.2.a.u	$2805$	$2$	2805.a	1.a	$1$	$8$	$8$	$22.398$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$-8$	$8$	$9$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
2805.2.a.v	$2805$	$2$	2805.a	1.a	$1$	$9$	$9$	$22.398$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$9$	$9$	$2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$

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Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
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.