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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 97 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
740.1.g.a	$740$	$1$	740.g	740.g	$2$	$1$	$1$	$0.369$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-185}) $	$\Q(\sqrt{185}) $	✓	$4$	$0$	$-1$	$0$	$-1$	$0$		$1$		$q-q^{2}+q^{4}-q^{5}-q^{8}-q^{9}+q^{10}+\cdots$
740.1.g.b	$740$	$1$	740.g	740.g	$2$	$1$	$1$	$0.369$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-185}) $	$\Q(\sqrt{185}) $	✓	$4$	$0$	$1$	$0$	$1$	$0$		$1$		$q+q^{2}+q^{4}+q^{5}+q^{8}-q^{9}+q^{10}+\cdots$
740.1.g.c	$740$	$1$	740.g	740.g	$2$	$2$	$2$	$0.369$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-185}) $	None	✓	$4$	$0$	$-2$	$0$	$2$	$0$		$1$		$q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+\beta q^{7}+\cdots$
740.1.g.d	$740$	$1$	740.g	740.g	$2$	$2$	$2$	$0.369$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-185}) $	None	✓	$4$	$0$	$2$	$0$	$-2$	$0$		$1$		$q+q^{2}-\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+\beta q^{7}+\cdots$
740.1.p.a	$740$	$1$	740.p	740.p	$4$	$2$	$1$	$0.369$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-q^{4}+iq^{5}+iq^{8}+iq^{9}+\cdots$
740.1.s.a	$740$	$1$	740.s	740.s	$4$	$2$	$1$	$0.369$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$-2$	$0$		$1$		$q-q^{2}+q^{4}-q^{5}-q^{8}+iq^{9}+q^{10}+\cdots$
740.1.t.a	$740$	$1$	740.t	185.j	$4$	$2$	$1$	$0.369$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$-2$	$2$	$0$		$1$		$q-q^{3}+q^{5}-iq^{7}-iq^{11}-q^{15}+\cdots$
740.1.t.b	$740$	$1$	740.t	185.j	$4$	$2$	$1$	$0.369$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$		$q+q^{3}+iq^{5}+iq^{7}-iq^{11}+iq^{15}+\cdots$
740.1.v.a	$740$	$1$	740.v	740.v	$6$	$2$	$1$	$0.369$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-1$	$0$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+q^{8}+\zeta_{6}q^{9}+\cdots$
740.1.v.b	$740$	$1$	740.v	740.v	$6$	$2$	$1$	$0.369$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-2$	$0$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}-q^{8}+\zeta_{6}q^{9}+\cdots$
740.1.bj.a	$740$	$1$	740.bj	740.aj	$12$	$4$	$1$	$0.369$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$2$	$0$		$1$		$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{5}+\cdots$
740.1.bm.a	$740$	$1$	740.bm	740.am	$12$	$4$	$1$	$0.369$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{5}+\cdots$
740.1.bu.a	$740$	$1$	740.bu	740.au	$18$	$6$	$1$	$0.369$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{8}q^{2}-\zeta_{18}^{7}q^{4}-\zeta_{18}^{5}q^{5}+\cdots$
740.1.bu.b	$740$	$1$	740.bu	740.au	$18$	$6$	$1$	$0.369$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$3$	$0$		$1$		$q-\zeta_{18}^{8}q^{2}-\zeta_{18}^{7}q^{4}+\zeta_{18}^{3}q^{5}+\cdots$
740.1.bw.a	$740$	$1$	740.bw	740.aw	$36$	$12$	$1$	$0.369$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{36}^{7}q^{2}+\zeta_{36}^{14}q^{4}+\zeta_{36}^{15}q^{5}+\cdots$
740.1.cb.a	$740$	$1$	740.cb	740.bb	$36$	$12$	$1$	$0.369$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{36}^{8}q^{2}+\zeta_{36}^{16}q^{4}+\zeta_{36}^{14}q^{5}+\cdots$
740.2.a.a	$740$	$2$	740.a	1.a	$1$	$1$	$1$	$5.909$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}-2q^{9}-3q^{11}-6q^{13}+\cdots$
740.2.a.b	$740$	$2$	740.a	1.a	$1$	$1$	$1$	$5.909$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}-2q^{9}-3q^{11}-4q^{13}+\cdots$
740.2.a.c	$740$	$2$	740.a	1.a	$1$	$1$	$1$	$5.909$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-q^{5}-3q^{7}+6q^{9}+5q^{11}+\cdots$
740.2.a.d	$740$	$2$	740.a	1.a	$1$	$2$	$2$	$5.909$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+q^{5}+(3+\beta )q^{7}+(1+\cdots)q^{9}+\cdots$
740.2.a.e	$740$	$2$	740.a	1.a	$1$	$3$	$3$	$5.909$	3.3.148.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}-q^{5}+(2\beta _{1}-\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots$
740.2.a.f	$740$	$2$	740.a	1.a	$1$	$4$	$4$	$5.909$	4.4.286164.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$4$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+q^{5}+(-1-\beta _{1})q^{7}+\cdots$
740.2.d.a	$740$	$2$	740.d	5.b	$2$	$18$	$18$	$5.909$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{13}q^{3}+\beta _{10}q^{5}-\beta _{8}q^{7}+(-2+\cdots)q^{9}+\cdots$
740.2.e.a	$740$	$2$	740.e	185.d	$2$	$20$	$20$	$5.909$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+\beta _{1}q^{5}-\beta _{4}q^{7}+(-1-\beta _{14}+\cdots)q^{9}+\cdots$
740.2.h.a	$740$	$2$	740.h	37.b	$2$	$2$	$2$	$5.909$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$6$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3q^{3}+iq^{5}-q^{7}+6q^{9}+3q^{11}+\cdots$
740.2.h.b	$740$	$2$	740.h	37.b	$2$	$12$	$12$	$5.909$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-6$	$0$	$-2$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{3})q^{3}-\beta _{6}q^{5}+\beta _{4}q^{7}+(1+\cdots)q^{9}+\cdots$
740.2.i.a	$740$	$2$	740.i	37.c	$3$	$14$	$7$	$5.909$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-7$	$4$		$3^{5}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{7}q^{3}+(-1+\beta _{10})q^{5}+(1+\beta _{5}+\cdots)q^{7}+\cdots$
740.2.i.b	$740$	$2$	740.i	37.c	$3$	$14$	$7$	$5.909$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$7$	$-2$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(1-\beta _{5})q^{5}+\beta _{11}q^{7}+(-\beta _{5}+\cdots)q^{9}+\cdots$
740.2.k.a	$740$	$2$	740.k	740.k	$4$	$2$	$1$	$5.909$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$-2$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-1+i)q^{2}-2iq^{4}+(-1-2i)q^{5}+\cdots$
740.2.k.b	$740$	$2$	740.k	740.k	$4$	$2$	$1$	$5.909$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(1-i)q^{2}-2iq^{4}+(2+i)q^{5}+(-2+\cdots)q^{8}+\cdots$
740.2.k.c	$740$	$2$	740.k	740.k	$4$	$216$	$108$	$5.909$		$_{}$	None	None		$8$	$0$	$0$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{4}]$
740.2.l.a	$740$	$2$	740.l	185.f	$4$	$6$	$3$	$5.909$	6.0.79423744.1	$_{}$	None	None		$2$	$0$	$0$	$2$	$-6$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{3}+(-1-2\beta _{4})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
740.2.l.b	$740$	$2$	740.l	185.f	$4$	$32$	$16$	$5.909$		$_{}$	None	None		$2$	$0$	$0$	$2$	$4$	$4$			$\mathrm{SU}(2)[C_{4}]$
740.2.m.a	$740$	$2$	740.m	740.m	$4$	$2$	$1$	$5.909$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$1$	$-2$	$0$	$-4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-1+i)q^{2}-2iq^{4}+(-2-i)q^{5}+\cdots$
740.2.m.b	$740$	$2$	740.m	740.m	$4$	$2$	$1$	$5.909$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(1-i)q^{2}-2iq^{4}+(2+i)q^{5}+(-2+\cdots)q^{8}+\cdots$
740.2.m.c	$740$	$2$	740.m	740.m	$4$	$216$	$108$	$5.909$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
740.2.n.a	$740$	$2$	740.n	20.e	$4$	$216$	$108$	$5.909$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
740.2.o.a	$740$	$2$	740.o	185.k	$4$	$6$	$3$	$5.909$	6.0.79423744.1	$_{}$	None	None		$2$	$0$	$0$	$-2$	$12$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{3}+(2+\beta _{4})q^{5}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots$
740.2.o.b	$740$	$2$	740.o	185.k	$4$	$32$	$16$	$5.909$		$_{}$	None	None		$2$	$0$	$0$	$-2$	$-12$	$4$			$\mathrm{SU}(2)[C_{4}]$
740.2.u.a	$740$	$2$	740.u	148.g	$4$	$152$	$76$	$5.909$		$_{}$	None	None		$4$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
740.2.x.a	$740$	$2$	740.x	37.e	$6$	$28$	$14$	$5.909$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{6}]$
740.2.ba.a	$740$	$2$	740.ba	185.l	$6$	$40$	$20$	$5.909$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-3$	$0$			$\mathrm{SU}(2)[C_{6}]$
740.2.bb.a	$740$	$2$	740.bb	185.n	$6$	$36$	$18$	$5.909$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$
740.2.bc.a	$740$	$2$	740.bc	37.f	$9$	$6$	$1$	$5.909$	$\Q(\zeta_{18})$	$_{}$	None	None		$2$	$0$	$0$	$-3$	$0$	$3$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\zeta_{18}-\zeta_{18}^{2}-\zeta_{18}^{3})q^{3}+(-\zeta_{18}^{2}+\cdots)q^{5}+\cdots$
740.2.bc.b	$740$	$2$	740.bc	37.f	$9$	$12$	$2$	$5.909$	12.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$12$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{9}]$	$q+(3+\beta _{1}+\beta _{2}-\beta _{4}-\beta _{5}-\beta _{6}+\beta _{8}+\cdots)q^{3}+\cdots$
740.2.bc.c	$740$	$2$	740.bc	37.f	$9$	$18$	$3$	$5.909$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-9$	$0$	$3$		$3$	$\mathrm{SU}(2)[C_{9}]$	$q+(-1+\beta _{5}-\beta _{6})q^{3}-\beta _{1}q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots$
740.2.bc.d	$740$	$2$	740.bc	37.f	$9$	$36$	$6$	$5.909$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$12$			$\mathrm{SU}(2)[C_{9}]$
740.2.be.a	$740$	$2$	740.be	148.l	$12$	$304$	$76$	$5.909$		$_{}$	None	None		$4$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$
740.2.bf.a	$740$	$2$	740.bf	185.p	$12$	$76$	$19$	$5.909$		$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$
740.2.bg.a	$740$	$2$	740.bg	740.ag	$12$	$4$	$1$	$5.909$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$-8$	$0$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots$

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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.