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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 1033 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
148.1.f.a	$148$	$1$	148.f	37.d	$4$	$2$	$1$	$0.074$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+iq^{3}-q^{7}-iq^{11}+(-1-i)q^{17}+\cdots$
229.1.d.a	$229$	$1$	229.d	229.d	$4$	$2$	$1$	$0.114$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$2$	$0$	$-2$	$1$		$q+q^{3}+iq^{4}-iq^{5}+(-1-i)q^{7}+\cdots$
229.1.d.b	$229$	$1$	229.d	229.d	$4$	$2$	$1$	$0.114$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$2$	$-2$	$0$	$0$	$1$		$q+(1-i)q^{2}-q^{3}-iq^{4}-iq^{5}+(-1+\cdots)q^{6}+\cdots$
261.1.f.a	$261$	$1$	261.f	29.c	$4$	$4$	$2$	$0.130$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{8}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}-q^{7}+\zeta_{8}^{3}q^{8}+\cdots$
283.1.b.b	$283$	$1$	283.b	283.b	$2$	$2$	$2$	$0.141$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\beta q^{2}+\beta q^{3}-q^{4}+\beta q^{5}+2q^{6}+\cdots$
296.1.k.a	$296$	$1$	296.k	37.d	$4$	$2$	$1$	$0.148$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q-iq^{3}+(-1-i)q^{5}-q^{7}-iq^{11}+\cdots$
331.1.b.b	$331$	$1$	331.b	331.b	$2$	$2$	$2$	$0.165$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\beta q^{2}-\beta q^{3}-q^{4}-q^{5}-2q^{6}+\beta q^{7}+\cdots$
333.1.p.a	$333$	$1$	333.p	111.i	$6$	$4$	$2$	$0.166$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$
344.1.b.a	$344$	$1$	344.b	43.b	$2$	$2$	$2$	$0.172$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{3}-\beta q^{5}+\beta q^{7}-q^{9}-q^{11}+\cdots$
371.1.k.a	$371$	$1$	371.k	371.k	$12$	$4$	$1$	$0.185$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$-2$	$-2$	$2$	$0$	$1$		$q+(-\zeta_{12}^{2}+\zeta_{12}^{5})q^{2}+(\zeta_{12}+\zeta_{12}^{4}+\cdots)q^{3}+\cdots$
371.1.k.b	$371$	$1$	371.k	371.k	$12$	$4$	$1$	$0.185$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-\zeta_{12}q^{4}+(\zeta_{12}^{2}+\zeta_{12}^{5})q^{5}+\zeta_{12}q^{7}+\cdots$
380.1.x.a	$380$	$1$	380.x	95.m	$12$	$4$	$1$	$0.190$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$0$	$-2$	$2$	$0$	$1$		$q+(-\zeta_{12}^{2}+\zeta_{12}^{5})q^{3}+\zeta_{12}^{2}q^{5}+\cdots$
404.1.f.a	$404$	$1$	404.f	101.c	$4$	$2$	$1$	$0.202$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$-2$	$2$	$2$	$1$		$q+(-1+i)q^{3}+q^{5}+(1-i)q^{7}-iq^{9}+\cdots$
408.1.u.a	$408$	$1$	408.u	51.f	$4$	$4$	$2$	$0.204$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{8}q^{3}-\zeta_{8}q^{5}+(-1-\zeta_{8}^{2})q^{7}+\cdots$
432.1.j.a	$432$	$1$	432.j	48.i	$4$	$4$	$2$	$0.216$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{7}+\cdots$
451.1.f.a	$451$	$1$	451.f	451.f	$4$	$4$	$2$	$0.225$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+q^{4}-\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots$
468.1.r.a	$468$	$1$	468.r	39.i	$6$	$4$	$2$	$0.234$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\beta _{3}q^{5}+(-1+\beta _{2})q^{7}+(\beta _{1}-\beta _{3})q^{11}+\cdots$
491.1.b.b	$491$	$1$	491.b	491.b	$2$	$2$	$2$	$0.245$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-\beta q^{2}-q^{3}-q^{4}+\beta q^{6}-\beta q^{7}+q^{11}+\cdots$
504.1.cu.a	$504$	$1$	504.cu	21.h	$6$	$4$	$2$	$0.252$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+(\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}-\beta _{1}q^{11}-q^{13}+\cdots$
527.1.f.a	$527$	$1$	527.f	527.f	$4$	$4$	$2$	$0.263$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$-4$	$0$	$1$		$q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}+(-1+\zeta_{8}^{2})q^{5}+\cdots$
553.1.p.b	$553$	$1$	553.p	553.p	$6$	$4$	$2$	$0.276$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		$4$	$0$	$-2$	$0$	$0$	$2$	$1$		$q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}+(-\beta _{1}+\beta _{3})q^{6}+\cdots$
563.1.b.b	$563$	$1$	563.b	563.b	$2$	$2$	$2$	$0.281$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$0$	$-2$	$0$	$2$	$1$		$q-\beta q^{2}-q^{3}-q^{4}-\beta q^{5}+\beta q^{6}+q^{7}+\cdots$
592.1.k.a	$592$	$1$	592.k	37.d	$4$	$2$	$1$	$0.295$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$-2$	$2$	$1$		$q+iq^{3}+(-1-i)q^{5}+q^{7}+iq^{11}+\cdots$
592.1.k.b	$592$	$1$	592.k	37.d	$4$	$2$	$1$	$0.295$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$2$	$1$		$q-iq^{3}+q^{7}+iq^{11}+(-1-i)q^{17}+\cdots$
592.1.z.a	$592$	$1$	592.z	148.i	$6$	$4$	$2$	$0.295$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+(\beta _{1}-\beta _{3})q^{3}-\beta _{2}q^{5}+(1-\beta _{2})q^{9}+\cdots$
612.1.j.a	$612$	$1$	612.j	51.f	$4$	$4$	$2$	$0.305$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{5}-\zeta_{8}^{3}q^{11}+q^{13}-\zeta_{8}^{3}q^{17}+\cdots$
643.1.b.b	$643$	$1$	643.b	643.b	$2$	$2$	$2$	$0.321$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$2$	$1$		$q-\beta q^{2}-\beta q^{3}-q^{4}-2q^{6}+q^{7}-q^{9}+\cdots$
657.1.u.a	$657$	$1$	657.u	219.j	$6$	$4$	$2$	$0.328$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$	$1$		$q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{4}+\beta _{1}q^{5}+\cdots$
679.1.j.a	$679$	$1$	679.j	679.j	$4$	$4$	$2$	$0.339$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{2}q^{2}+(\zeta_{8}-\zeta_{8}^{3})q^{3}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{6}+\cdots$
684.1.q.a	$684$	$1$	684.q	76.g	$6$	$8$	$4$	$0.341$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}+(\zeta_{24}^{5}+\zeta_{24}^{11}+\cdots)q^{5}+\cdots$
688.1.b.b	$688$	$1$	688.b	43.b	$2$	$2$	$2$	$0.343$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta q^{3}-\beta q^{5}-\beta q^{7}-q^{9}+q^{11}+\cdots$
695.1.k.a	$695$	$1$	695.k	695.k	$12$	$4$	$1$	$0.347$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$2$	$0$	$0$	$2$	$1$		$q+(\zeta_{12}^{2}+\zeta_{12}^{5})q^{2}-\zeta_{12}q^{4}-\zeta_{12}q^{5}+\cdots$
733.1.d.a	$733$	$1$	733.d	733.d	$4$	$2$	$1$	$0.366$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q-q^{3}-iq^{4}+(-1+i)q^{5}+iq^{12}+\cdots$
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		$2$	$0$	$0$	$2$	$0$	$0$	$1$		$q+q^{3}+iq^{5}+iq^{7}-iq^{11}+iq^{15}+\cdots$
744.1.bb.a	$744$	$1$	744.bb	93.h	$6$	$4$	$2$	$0.371$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-\beta _{2}q^{3}+\beta _{1}q^{5}+(-1+\beta _{2})q^{9}+\beta _{1}q^{11}+\cdots$
748.1.i.a	$748$	$1$	748.i	187.f	$4$	$4$	$2$	$0.373$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$4$	$0$	$0$	$1$		$q+(1-\zeta_{8}^{2})q^{3}-\zeta_{8}^{3}q^{7}-\zeta_{8}^{2}q^{9}+\cdots$
751.1.b.b	$751$	$1$	751.b	751.b	$2$	$2$	$2$	$0.375$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}-\beta q^{3}+\beta q^{6}+\beta q^{7}+q^{8}-q^{9}+\cdots$
755.1.o.a	$755$	$1$	755.o	755.o	$12$	$4$	$1$	$0.377$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-\zeta_{12}q^{4}+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{9}-\zeta_{12}^{2}q^{11}+\cdots$
760.1.bt.a	$760$	$1$	760.bt	95.m	$12$	$4$	$1$	$0.379$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(\zeta_{12}-\zeta_{12}^{4})q^{3}-\zeta_{12}q^{5}-\zeta_{12}^{5}q^{9}+\cdots$
765.1.j.a	$765$	$1$	765.j	255.i	$4$	$4$	$2$	$0.382$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{5}+\zeta_{8}^{3}q^{7}-\zeta_{8}^{2}q^{8}+\cdots$
765.1.j.b	$765$	$1$	765.j	255.i	$4$	$4$	$2$	$0.382$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{5}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{8}+\cdots$
765.1.m.a	$765$	$1$	765.m	85.f	$4$	$4$	$2$	$0.382$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}q^{5}+\zeta_{8}^{2}q^{7}+\zeta_{8}^{3}q^{8}+\cdots$
765.1.r.a	$765$	$1$	765.r	85.i	$4$	$4$	$2$	$0.382$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{3}q^{5}-q^{7}+\zeta_{8}^{3}q^{8}+\cdots$
765.1.bn.a	$765$	$1$	765.bn	765.an	$12$	$4$	$1$	$0.382$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$-2$	$-2$	$0$	$-2$	$1$		$q+(-\zeta_{12}^{2}-\zeta_{12}^{5})q^{2}-\zeta_{12}^{2}q^{3}+\cdots$
765.1.bn.b	$765$	$1$	765.bn	765.an	$12$	$4$	$1$	$0.382$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$0$	$-2$	$-2$	$2$	$1$		$q-\zeta_{12}^{2}q^{3}+\zeta_{12}q^{4}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{2}q^{7}+\cdots$
765.1.bs.a	$765$	$1$	765.bs	765.as	$12$	$4$	$1$	$0.382$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{3}+\zeta_{12}^{5}q^{4}-\zeta_{12}^{5}q^{5}-\zeta_{12}q^{7}+\cdots$
765.1.bs.b	$765$	$1$	765.bs	765.as	$12$	$4$	$1$	$0.382$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$2$	$0$	$2$	$0$	$1$		$q+(\zeta_{12}-\zeta_{12}^{4})q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{5}q^{4}+\cdots$
771.1.e.a	$771$	$1$	771.e	771.e	$4$	$2$	$1$	$0.385$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$-2$	$0$	$2$	$1$		$q-iq^{2}-q^{3}+iq^{6}+(1+i)q^{7}-iq^{8}+\cdots$
771.1.e.b	$771$	$1$	771.e	771.e	$4$	$2$	$1$	$0.385$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$2$	$1$		$q+iq^{2}-iq^{3}+q^{6}+(1+i)q^{7}+iq^{8}+\cdots$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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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.