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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 (1-50 of 103 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
204.1.g.a	$204$	$1$	204.g	51.c	$2$	$1$	$1$	$0.102$	$\Q$	$D_{3}$	$\Q(\sqrt{-51}) $	None	✓	$2$	$0$	$0$	$-1$	$1$	$0$		$1$		$q-q^{3}+q^{5}+q^{9}+q^{11}-q^{13}-q^{15}+\cdots$
204.1.g.b	$204$	$1$	204.g	51.c	$2$	$1$	$1$	$0.102$	$\Q$	$D_{3}$	$\Q(\sqrt{-51}) $	None	✓	$2$	$0$	$0$	$1$	$-1$	$0$		$1$		$q+q^{3}-q^{5}+q^{9}-q^{11}-q^{13}-q^{15}+\cdots$
204.2.a.a	$204$	$2$	204.a	1.a	$1$	$1$	$1$	$1.629$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+4q^{7}+q^{9}+3q^{11}+3q^{13}+\cdots$
204.2.a.b	$204$	$2$	204.a	1.a	$1$	$1$	$1$	$1.629$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+5q^{11}-5q^{13}+\cdots$
204.2.b.a	$204$	$2$	204.b	17.b	$2$	$2$	$2$	$1.629$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+iq^{5}+2iq^{7}-q^{9}+3iq^{11}+\cdots$
204.2.c.a	$204$	$2$	204.c	12.b	$2$	$32$	$32$	$1.629$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
204.2.h.a	$204$	$2$	204.h	204.h	$2$	$8$	$8$	$1.629$	8.0.$\cdots$.11	$_{}$	$\Q(\sqrt{-17}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{3}q^{2}+\beta _{1}q^{3}-2q^{4}-\beta _{6}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots$
204.2.h.b	$204$	$2$	204.h	204.h	$2$	$24$	$24$	$1.629$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
204.2.j.a	$204$	$2$	204.j	17.c	$4$	$4$	$2$	$1.629$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$8$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{3}+(2-\zeta_{8}+2\zeta_{8}^{2})q^{5}+(-1+\cdots)q^{7}+\cdots$
204.2.l.a	$204$	$2$	204.l	204.l	$4$	$64$	$32$	$1.629$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
204.2.o.a	$204$	$2$	204.o	17.d	$8$	$16$	$4$	$1.629$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q-\beta _{13}q^{3}+(-1+\beta _{1}-\beta _{2}+\beta _{5}-\beta _{7}+\cdots)q^{5}+\cdots$
204.2.p.a	$204$	$2$	204.p	204.p	$8$	$128$	$32$	$1.629$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
204.2.q.a	$204$	$2$	204.q	51.i	$16$	$48$	$6$	$1.629$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
204.2.r.a	$204$	$2$	204.r	68.i	$16$	$144$	$18$	$1.629$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
204.3.d.a	$204$	$3$	204.d	3.b	$2$	$10$	$10$	$5.559$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$-4$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}-\beta _{6}q^{5}+\beta _{9}q^{7}+(-3+\beta _{1}+\cdots)q^{9}+\cdots$
204.3.e.a	$204$	$3$	204.e	68.d	$2$	$36$	$36$	$5.559$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
204.3.f.a	$204$	$3$	204.f	4.b	$2$	$32$	$32$	$5.559$		$_{}$	None	None		$2$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
204.3.g.a	$204$	$3$	204.g	51.c	$2$	$2$	$2$	$5.559$	$\Q(\sqrt{17}) $	$_{}$	$\Q(\sqrt{-51}) $	None	✓	$2$	$0$	$0$	$-6$	$-7$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}+(-3-\beta )q^{5}+9q^{9}+(1+3\beta )q^{11}+\cdots$
204.3.g.b	$204$	$3$	204.g	51.c	$2$	$2$	$2$	$5.559$	$\Q(\sqrt{17}) $	$_{}$	$\Q(\sqrt{-51}) $	None	✓	$2$	$0$	$0$	$6$	$7$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}+(3+\beta )q^{5}+9q^{9}+(-1-3\beta )q^{11}+\cdots$
204.3.g.c	$204$	$3$	204.g	51.c	$2$	$8$	$8$	$5.559$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{2})q^{3}+(\beta _{2}+\beta _{4})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots$
204.3.i.a	$204$	$3$	204.i	51.f	$4$	$4$	$2$	$5.559$	$\Q(i, \sqrt{17})$	$_{}$	None	None		$4$	$0$	$0$	$-2$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{1}+2\beta _{3})q^{5}+\cdots$
204.3.i.b	$204$	$3$	204.i	51.f	$4$	$20$	$10$	$5.559$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$6$	$0$	$-4$		$2^{9}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{4}q^{3}+\beta _{10}q^{5}-\beta _{5}q^{7}+(-2\beta _{3}+\cdots)q^{9}+\cdots$
204.3.k.a	$204$	$3$	204.k	68.f	$4$	$72$	$36$	$5.559$		$_{}$	None	None		$4$	$0$	$0$	$0$	$8$	$0$			$\mathrm{SU}(2)[C_{4}]$
204.3.m.a	$204$	$3$	204.m	51.g	$8$	$48$	$12$	$5.559$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
204.3.n.a	$204$	$3$	204.n	68.g	$8$	$144$	$36$	$5.559$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
204.3.s.a	$204$	$3$	204.s	17.e	$16$	$48$	$6$	$5.559$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
204.3.t.a	$204$	$3$	204.t	204.t	$16$	$544$	$68$	$5.559$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
204.4.a.a	$204$	$4$	204.a	1.a	$1$	$1$	$1$	$12.036$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$3$	$-3$	$-16$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-3q^{5}-2^{4}q^{7}+9q^{9}-57q^{11}+\cdots$
204.4.a.b	$204$	$4$	204.a	1.a	$1$	$2$	$2$	$12.036$	$\Q(\sqrt{201}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-6$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+(1+\beta )q^{5}-2\beta q^{7}+9q^{9}+\cdots$
204.4.a.c	$204$	$4$	204.a	1.a	$1$	$2$	$2$	$12.036$	$\Q(\sqrt{217}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$6$	$19$	$18$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+(10-\beta )q^{5}+(10-2\beta )q^{7}+\cdots$
204.4.a.d	$204$	$4$	204.a	1.a	$1$	$3$	$3$	$12.036$	3.3.21324.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-9$	$-19$	$-8$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-3q^{3}+(-7-\beta _{1}+\beta _{2})q^{5}+(-3+\cdots)q^{7}+\cdots$
204.4.b.a	$204$	$4$	204.b	17.b	$2$	$10$	$10$	$12.036$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{11}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-\beta _{3}q^{5}+(\beta _{1}+\beta _{2}+\beta _{3})q^{7}+\cdots$
204.4.c.a	$204$	$4$	204.c	12.b	$2$	$96$	$96$	$12.036$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
204.4.h.a	$204$	$4$	204.h	204.h	$2$	$8$	$8$	$12.036$	8.0.$\cdots$.11	$_{}$	$\Q(\sqrt{-17}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+2\beta _{2}q^{2}+(-\beta _{3}-\beta _{5})q^{3}-8q^{4}+\cdots$
204.4.h.b	$204$	$4$	204.h	204.h	$2$	$96$	$96$	$12.036$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
204.4.j.a	$204$	$4$	204.j	17.c	$4$	$20$	$10$	$12.036$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$-8$		$2^{18}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{4}q^{3}+\beta _{12}q^{5}+(\beta _{3}+\beta _{7})q^{7}-9\beta _{2}q^{9}+\cdots$
204.4.l.a	$204$	$4$	204.l	204.l	$4$	$208$	$104$	$12.036$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
204.4.o.a	$204$	$4$	204.o	17.d	$8$	$32$	$8$	$12.036$		$_{}$	None	None		$2$	$0$	$0$	$0$	$32$	$0$			$\mathrm{SU}(2)[C_{8}]$
204.4.p.a	$204$	$4$	204.p	204.p	$8$	$416$	$104$	$12.036$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
204.4.q.a	$204$	$4$	204.q	51.i	$16$	$144$	$18$	$12.036$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
204.4.r.a	$204$	$4$	204.r	68.i	$16$	$432$	$54$	$12.036$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
204.5.d.a	$204$	$5$	204.d	3.b	$2$	$22$	$22$	$21.087$		$_{}$	None	None		$2$	$0$	$0$	$-10$	$0$	$188$			$\mathrm{SU}(2)[C_{2}]$
204.5.e.a	$204$	$5$	204.e	68.d	$2$	$72$	$72$	$21.087$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
204.5.f.a	$204$	$5$	204.f	4.b	$2$	$64$	$64$	$21.087$		$_{}$	None	None		$2$	$0$	$-12$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
204.5.g.a	$204$	$5$	204.g	51.c	$2$	$2$	$2$	$21.087$	$\Q(\sqrt{17}) $	$_{}$	$\Q(\sqrt{-51}) $	None	✓	$2$	$0$	$0$	$-18$	$-1$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q-9q^{3}+(3-7\beta )q^{5}+3^{4}q^{9}+(-101+\cdots)q^{11}+\cdots$
204.5.g.b	$204$	$5$	204.g	51.c	$2$	$2$	$2$	$21.087$	$\Q(\sqrt{17}) $	$_{}$	$\Q(\sqrt{-51}) $	None	✓	$2$	$0$	$0$	$18$	$1$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+9q^{3}+(-3+7\beta )q^{5}+3^{4}q^{9}+(101+\cdots)q^{11}+\cdots$
204.5.g.c	$204$	$5$	204.g	51.c	$2$	$20$	$20$	$21.087$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{9}\cdot 3^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+\beta _{12}q^{5}+(-\beta _{2}-\beta _{13})q^{7}+\cdots$
204.5.i.a	$204$	$5$	204.i	51.f	$4$	$48$	$24$	$21.087$		$_{}$	None	None		$4$	$0$	$0$	$-8$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
204.5.m.a	$204$	$5$	204.m	51.g	$8$	$96$	$24$	$21.087$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
204.5.s.a	$204$	$5$	204.s	17.e	$16$	$96$	$12$	$21.087$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$

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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.