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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 69 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
671.1.d.a	$671$	$1$	671.d	671.d	$2$	$1$	$1$	$0.335$	$\Q$	$D_{3}$	$\Q(\sqrt{-671}) $	None	✓	$2$	$0$	$-1$	$-1$	$2$	$-1$		$1$		$q-q^{2}-q^{3}+2q^{5}+q^{6}-q^{7}+q^{8}+\cdots$
671.1.d.b	$671$	$1$	671.d	671.d	$2$	$1$	$1$	$0.335$	$\Q$	$D_{3}$	$\Q(\sqrt{-671}) $	None	✓	$2$	$0$	$1$	$-1$	$2$	$1$		$1$		$q+q^{2}-q^{3}+2q^{5}-q^{6}+q^{7}-q^{8}+\cdots$
671.1.d.c	$671$	$1$	671.d	671.d	$2$	$2$	$2$	$0.335$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-671}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$4$		$1$		$q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-\beta q^{5}+\cdots$
671.1.d.d	$671$	$1$	671.d	671.d	$2$	$2$	$2$	$0.335$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-671}) $	None	✓	$2$	$0$	$1$	$-1$	$-1$	$-4$		$1$		$q+(1-\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-\beta q^{5}+\cdots$
671.1.d.e	$671$	$1$	671.d	671.d	$2$	$4$	$4$	$0.335$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-671}) $	None	✓	$2$	$0$	$-1$	$1$	$-2$	$4$		$1$		$q-\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
671.1.d.f	$671$	$1$	671.d	671.d	$2$	$4$	$4$	$0.335$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-671}) $	None	✓	$2$	$0$	$1$	$1$	$-2$	$-4$		$1$		$q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
671.1.p.a	$671$	$1$	671.p	671.p	$6$	$4$	$2$	$0.335$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{5}-\zeta_{12}q^{7}+\zeta_{12}^{3}q^{8}+\cdots$
671.2.a.a	$671$	$2$	671.a	1.a	$1$	$5$	$5$	$5.358$	5.5.24217.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{4})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots$
671.2.a.b	$671$	$2$	671.a	1.a	$1$	$6$	$6$	$5.358$	6.6.2661761.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}-\beta _{1}q^{3}-\beta _{5}q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$
671.2.a.c	$671$	$2$	671.a	1.a	$1$	$19$	$19$	$5.358$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$5$	$0$	$0$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots$
671.2.a.d	$671$	$2$	671.a	1.a	$1$	$21$	$21$	$5.358$		$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$7$	$5$	$-$		$\mathrm{SU}(2)$
671.2.c.a	$671$	$2$	671.c	61.b	$2$	$52$	$52$	$5.358$		$_{}$	None	None		$2$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
671.2.e.a	$671$	$2$	671.e	61.c	$3$	$52$	$26$	$5.358$		$_{}$	None	None		$2$	$0$	$-2$	$2$	$0$	$-7$			$\mathrm{SU}(2)[C_{3}]$
671.2.e.b	$671$	$2$	671.e	61.c	$3$	$52$	$26$	$5.358$		$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$5$			$\mathrm{SU}(2)[C_{3}]$
671.2.f.a	$671$	$2$	671.f	671.f	$4$	$120$	$60$	$5.358$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
671.2.h.a	$671$	$2$	671.h	671.h	$5$	$4$	$1$	$5.358$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$-3$	$1$	$4$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10})q^{2}+\zeta_{10}q^{3}+(1+\zeta_{10}^{2}+\cdots)q^{4}+\cdots$
671.2.h.b	$671$	$2$	671.h	671.h	$5$	$236$	$59$	$5.358$		$_{}$	None	None		$2$	$0$	$2$	$-2$	$-6$	$1$			$\mathrm{SU}(2)[C_{5}]$
671.2.i.a	$671$	$2$	671.i	61.e	$5$	$108$	$27$	$5.358$		$_{}$	None	None		$2$	$0$	$-2$	$-2$	$4$	$8$			$\mathrm{SU}(2)[C_{5}]$
671.2.i.b	$671$	$2$	671.i	61.e	$5$	$108$	$27$	$5.358$		$_{}$	None	None		$2$	$0$	$0$	$-2$	$4$	$10$			$\mathrm{SU}(2)[C_{5}]$
671.2.j.a	$671$	$2$	671.j	11.c	$5$	$4$	$1$	$5.358$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$2$	$6$	$-1$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(2-2\zeta_{10}+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+\cdots$
671.2.j.b	$671$	$2$	671.j	11.c	$5$	$108$	$27$	$5.358$		$_{}$	None	None		$2$	$0$	$-3$	$5$	$7$	$-6$			$\mathrm{SU}(2)[C_{5}]$
671.2.j.c	$671$	$2$	671.j	11.c	$5$	$128$	$32$	$5.358$		$_{}$	None	None		$2$	$0$	$-5$	$-17$	$-8$	$-3$			$\mathrm{SU}(2)[C_{5}]$
671.2.k.a	$671$	$2$	671.k	671.k	$5$	$4$	$1$	$5.358$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$2$	$5$	$4$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}+\zeta_{10}^{3})q^{2}+(2-2\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots$
671.2.k.b	$671$	$2$	671.k	671.k	$5$	$236$	$59$	$5.358$		$_{}$	None	None		$2$	$0$	$-3$	$-6$	$-16$	$1$			$\mathrm{SU}(2)[C_{5}]$
671.2.l.a	$671$	$2$	671.l	671.l	$5$	$4$	$1$	$5.358$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$-3$	$0$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{10}^{2})q^{2}+(1+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{3}+\cdots$
671.2.l.b	$671$	$2$	671.l	671.l	$5$	$236$	$59$	$5.358$		$_{}$	None	None		$2$	$0$	$2$	$-6$	$4$	$-4$			$\mathrm{SU}(2)[C_{5}]$
671.2.m.a	$671$	$2$	671.m	671.m	$5$	$4$	$1$	$5.358$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$2$	$1$	$-6$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots$
671.2.m.b	$671$	$2$	671.m	671.m	$5$	$236$	$59$	$5.358$		$_{}$	None	None		$2$	$0$	$-8$	$-2$	$4$	$-9$			$\mathrm{SU}(2)[C_{5}]$
671.2.o.a	$671$	$2$	671.o	61.f	$6$	$100$	$50$	$5.358$		$_{}$	None	None		$2$	$0$	$0$	$4$	$-6$	$6$			$\mathrm{SU}(2)[C_{6}]$
671.2.q.a	$671$	$2$	671.q	671.q	$10$	$240$	$60$	$5.358$		$_{}$	None	None		$2$	$0$	$0$	$-1$	$0$	$-5$			$\mathrm{SU}(2)[C_{10}]$
671.2.x.a	$671$	$2$	671.x	671.x	$10$	$240$	$60$	$5.358$		$_{}$	None	None		$4$	$0$	$0$	$-6$	$-10$	$0$			$\mathrm{SU}(2)[C_{10}]$
671.2.ba.a	$671$	$2$	671.ba	671.aa	$10$	$240$	$60$	$5.358$		$_{}$	None	None		$2$	$0$	$-5$	$-1$	$0$	$-5$			$\mathrm{SU}(2)[C_{10}]$
671.2.bc.a	$671$	$2$	671.bc	61.g	$10$	$208$	$52$	$5.358$		$_{}$	None	None		$2$	$0$	$0$	$-4$	$-10$	$-30$			$\mathrm{SU}(2)[C_{10}]$
671.2.bd.a	$671$	$2$	671.bd	671.ad	$10$	$240$	$60$	$5.358$		$_{}$	None	None		$2$	$0$	$-5$	$-1$	$0$	$-5$			$\mathrm{SU}(2)[C_{10}]$
671.2.bf.a	$671$	$2$	671.bf	671.af	$10$	$240$	$60$	$5.358$		$_{}$	None	None		$2$	$0$	$-5$	$-6$	$-5$	$0$			$\mathrm{SU}(2)[C_{10}]$
671.2.bj.a	$671$	$2$	671.bj	671.aj	$12$	$240$	$60$	$5.358$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{12}]$
671.2.bk.a	$671$	$2$	671.bk	671.ak	$15$	$480$	$60$	$5.358$		$_{}$	None	None		$2$	$0$	$-3$	$-2$	$-16$	$-11$			$\mathrm{SU}(2)[C_{15}]$
671.2.bl.a	$671$	$2$	671.bl	671.al	$15$	$480$	$60$	$5.358$		$_{}$	None	None		$2$	$0$	$-8$	$-2$	$-6$	$-6$			$\mathrm{SU}(2)[C_{15}]$
671.2.bm.a	$671$	$2$	671.bm	671.am	$15$	$480$	$60$	$5.358$		$_{}$	None	None		$4$	$0$	$-3$	$-12$	$-1$	$-6$			$\mathrm{SU}(2)[C_{15}]$
671.2.bn.a	$671$	$2$	671.bn	61.i	$15$	$208$	$26$	$5.358$		$_{}$	None	None		$2$	$0$	$0$	$-2$	$-10$	$-10$			$\mathrm{SU}(2)[C_{15}]$
671.2.bn.b	$671$	$2$	671.bn	61.i	$15$	$208$	$26$	$5.358$		$_{}$	None	None		$2$	$0$	$2$	$-2$	$-10$	$-8$			$\mathrm{SU}(2)[C_{15}]$
671.2.bo.a	$671$	$2$	671.bo	671.ao	$15$	$480$	$60$	$5.358$		$_{}$	None	None		$2$	$0$	$-8$	$-2$	$-1$	$-6$			$\mathrm{SU}(2)[C_{15}]$
671.2.bp.a	$671$	$2$	671.bp	671.ap	$15$	$480$	$60$	$5.358$		$_{}$	None	None		$2$	$0$	$-8$	$-12$	$-6$	$-1$			$\mathrm{SU}(2)[C_{15}]$
671.2.br.a	$671$	$2$	671.br	671.ar	$20$	$480$	$60$	$5.358$		$_{}$	None	None		$2$	$0$	$-10$	$0$	$-10$	$-10$			$\mathrm{SU}(2)[C_{20}]$
671.2.bt.a	$671$	$2$	671.bt	671.at	$20$	$480$	$60$	$5.358$		$_{}$	None	None		$2$	$0$	$-10$	$-10$	$-10$	$-20$			$\mathrm{SU}(2)[C_{20}]$
671.2.bv.a	$671$	$2$	671.bv	671.av	$20$	$480$	$60$	$5.358$		$_{}$	None	None		$2$	$0$	$-10$	$-10$	$0$	$-10$			$\mathrm{SU}(2)[C_{20}]$
671.2.bw.a	$671$	$2$	671.bw	671.aw	$20$	$480$	$60$	$5.358$		$_{}$	None	None		$4$	$0$	$0$	$-20$	$-20$	$0$			$\mathrm{SU}(2)[C_{20}]$
671.2.by.a	$671$	$2$	671.by	671.ay	$20$	$480$	$60$	$5.358$		$_{}$	None	None		$2$	$0$	$-10$	$-10$	$-10$	$-10$			$\mathrm{SU}(2)[C_{20}]$
671.2.cb.a	$671$	$2$	671.cb	671.bb	$20$	$480$	$60$	$5.358$		$_{}$	None	None		$4$	$0$	$-10$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{20}]$
671.2.ce.a	$671$	$2$	671.ce	671.be	$30$	$480$	$60$	$5.358$		$_{}$	None	None		$2$	$0$	$-4$	$-2$	$0$	$2$			$\mathrm{SU}(2)[C_{30}]$

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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.