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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 10721 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
68.1.f.a	$68$	$1$	68.f	68.f	$4$	$2$	$1$	$0.034$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots$
112.1.l.a	$112$	$1$	112.l	112.l	$4$	$2$	$1$	$0.056$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{2}-q^{4}+iq^{7}-iq^{8}-iq^{9}+\cdots$
117.1.j.a	$117$	$1$	117.j	13.d	$4$	$2$	$1$	$0.058$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+iq^{4}+(-1-i)q^{7}-iq^{13}-q^{16}+\cdots$
136.1.j.a	$136$	$1$	136.j	136.j	$4$	$2$	$1$	$0.068$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-iq^{2}+(-1-i)q^{3}-q^{4}+(-1+i+\cdots)q^{6}+\cdots$
145.1.f.a	$145$	$1$	145.f	145.f	$4$	$2$	$1$	$0.072$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{4}-iq^{5}+iq^{9}+(-1-i)q^{11}+\cdots$
145.1.h.a	$145$	$1$	145.h	145.h	$4$	$2$	$1$	$0.072$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{29}) $		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-iq^{4}-iq^{5}+(-1+i)q^{7}+iq^{9}+\cdots$
148.1.f.a	$148$	$1$	148.f	37.d	$4$	$2$	$1$	$0.074$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+iq^{3}-q^{7}-iq^{11}+(-1-i)q^{17}+\cdots$
160.1.p.a	$160$	$1$	160.p	5.c	$4$	$2$	$1$	$0.080$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{5}+iq^{9}+(-1+i)q^{13}+(-1+\cdots)q^{17}+\cdots$
165.1.l.a	$165$	$1$	165.l	165.l	$4$	$2$	$1$	$0.082$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-q^{3}+iq^{4}+iq^{5}+q^{9}-iq^{11}+\cdots$
165.1.l.b	$165$	$1$	165.l	165.l	$4$	$2$	$1$	$0.082$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}+iq^{4}-iq^{5}-q^{9}+iq^{11}+\cdots$
180.1.m.a	$180$	$1$	180.m	60.l	$4$	$4$	$2$	$0.090$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}-\zeta_{8}q^{8}+\cdots$
219.1.f.a	$219$	$1$	219.f	219.f	$4$	$2$	$1$	$0.109$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-iq^{3}+q^{4}+(-1+i)q^{7}-q^{9}-iq^{12}+\cdots$
225.1.g.a	$225$	$1$	225.g	5.c	$4$	$2$	$1$	$0.112$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-15}) $	$\Q(\sqrt{5}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{4}-q^{16}-iq^{19}-q^{31}+iq^{49}+\cdots$
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		$2$	$0$	$2$	$-2$	$0$	$0$	$1$		$q+(1-i)q^{2}-q^{3}-iq^{4}-iq^{5}+(-1+\cdots)q^{6}+\cdots$
240.1.bm.a	$240$	$1$	240.bm	240.am	$4$	$4$	$2$	$0.120$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}+\cdots$
255.1.i.a	$255$	$1$	255.i	255.i	$4$	$4$	$2$	$0.127$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{3}q^{3}-q^{4}+\cdots$
16.2.e.a	$16$	$2$	16.e	16.e	$4$	$2$	$1$	$0.128$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$-2$	$-2$	$-2$	$0$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-i)q^{2}+(-1+i)q^{3}+2iq^{4}+\cdots$
260.1.l.a	$260$	$1$	260.l	260.l	$4$	$2$	$1$	$0.130$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-iq^{2}-q^{4}+q^{5}+iq^{8}-iq^{9}-iq^{10}+\cdots$
260.1.s.a	$260$	$1$	260.s	260.s	$4$	$2$	$1$	$0.130$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}+iq^{5}-q^{8}+iq^{9}-iq^{10}+\cdots$
261.1.f.a	$261$	$1$	261.f	29.c	$4$	$4$	$2$	$0.130$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{8}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}-q^{7}+\zeta_{8}^{3}q^{8}+\cdots$
273.1.o.a	$273$	$1$	273.o	273.o	$4$	$2$	$1$	$0.136$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{3}+iq^{4}-iq^{7}-q^{9}-q^{12}+\cdots$
273.1.o.b	$273$	$1$	273.o	273.o	$4$	$2$	$1$	$0.136$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q-iq^{3}+iq^{4}+q^{7}-q^{9}+q^{12}-iq^{13}+\cdots$
291.1.g.a	$291$	$1$	291.g	291.g	$4$	$2$	$1$	$0.145$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q-iq^{3}-q^{4}+(1-i)q^{7}-q^{9}+iq^{12}+\cdots$
296.1.k.a	$296$	$1$	296.k	37.d	$4$	$2$	$1$	$0.148$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q-iq^{3}+(-1-i)q^{5}-q^{7}-iq^{11}+\cdots$
300.1.l.a	$300$	$1$	300.l	60.l	$4$	$4$	$2$	$0.150$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{3}) $		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-q^{6}+\cdots$
20.2.e.a	$20$	$2$	20.e	20.e	$4$	$2$	$1$	$0.160$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$-4$	$0$	$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-1-i)q^{2}+2iq^{4}+(-2+i)q^{5}+\cdots$
320.1.p.a	$320$	$1$	320.p	5.c	$4$	$2$	$1$	$0.160$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{5}+iq^{9}+(1-i)q^{13}+(-1-i+\cdots)q^{17}+\cdots$
323.1.g.a	$323$	$1$	323.g	323.g	$4$	$2$	$1$	$0.161$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$-2$	$1$		$q-q^{4}+(1+i)q^{5}+(-1+i)q^{7}+iq^{9}+\cdots$
328.1.k.a	$328$	$1$	328.k	328.k	$4$	$2$	$1$	$0.164$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q-iq^{2}+(1-i)q^{3}-q^{4}+(-1-i+\cdots)q^{6}+\cdots$
333.1.i.a	$333$	$1$	333.i	37.d	$4$	$2$	$1$	$0.166$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{4}+(1-i)q^{13}-q^{16}+(-1+i+\cdots)q^{19}+\cdots$
360.1.u.a	$360$	$1$	360.u	40.i	$4$	$4$	$2$	$0.180$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+(-1+\cdots)q^{7}+\cdots$
368.1.k.a	$368$	$1$	368.k	368.k	$4$	$2$	$1$	$0.184$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q-iq^{2}+(1-i)q^{3}-q^{4}+(-1-i+\cdots)q^{6}+\cdots$
368.1.k.b	$368$	$1$	368.k	368.k	$4$	$4$	$2$	$0.184$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+\zeta_{12}^{5}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-\zeta_{12}^{4}q^{4}+\cdots$
388.1.g.a	$388$	$1$	388.g	388.g	$4$	$2$	$1$	$0.194$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+iq^{2}-q^{4}+(1+i)q^{5}-iq^{8}-q^{9}+\cdots$
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		$4$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{8}q^{3}-\zeta_{8}q^{5}+(-1-\zeta_{8}^{2})q^{7}+\cdots$
416.1.t.a	$416$	$1$	416.t	13.d	$4$	$2$	$1$	$0.208$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+(1+i)q^{5}-q^{9}+iq^{13}-iq^{17}+\cdots$
432.1.j.a	$432$	$1$	432.j	48.i	$4$	$4$	$2$	$0.216$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{7}+\cdots$
445.1.g.a	$445$	$1$	445.g	445.g	$4$	$2$	$1$	$0.222$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{89}) $		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+(-1-i)q^{2}+iq^{4}-iq^{5}-q^{8}+\cdots$
448.1.l.a	$448$	$1$	448.l	112.l	$4$	$2$	$1$	$0.224$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{7}-iq^{9}+(1+i)q^{11}+iq^{25}+\cdots$
451.1.f.a	$451$	$1$	451.f	451.f	$4$	$4$	$2$	$0.225$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+q^{4}-\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots$
452.1.e.a	$452$	$1$	452.e	452.e	$4$	$2$	$1$	$0.226$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$-2$	$0$	$1$		$q+q^{2}+q^{4}+(-1-i)q^{5}+q^{8}-iq^{9}+\cdots$
468.1.o.a	$468$	$1$	468.o	156.l	$4$	$4$	$2$	$0.234$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{8}+q^{13}+\cdots$
30.2.e.a	$30$	$2$	30.e	15.e	$4$	$4$	$2$	$0.240$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$-4$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
496.1.j.a	$496$	$1$	496.j	496.j	$4$	$2$	$1$	$0.248$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-2$	$0$	$2$	$0$	$1$		$q-q^{2}+q^{4}+(1+i)q^{5}-iq^{7}-q^{8}+\cdots$
496.1.j.b	$496$	$1$	496.j	496.j	$4$	$4$	$2$	$0.248$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$2$	$0$	$-2$	$0$	$1$		$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+(\zeta_{12}^{4}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots$
505.1.g.a	$505$	$1$	505.g	505.g	$4$	$2$	$1$	$0.252$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+iq^{4}+q^{5}+iq^{9}+(-1-i)q^{11}+\cdots$
505.1.h.a	$505$	$1$	505.h	505.h	$4$	$2$	$1$	$0.252$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{101}) $		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+iq^{4}+q^{5}-iq^{9}+(-1+i)q^{13}+\cdots$
512.1.f.a	$512$	$1$	512.f	16.f	$4$	$2$	$1$	$0.256$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+(-1-i)q^{5}-iq^{9}+(1-i)q^{13}+\cdots$

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Elliptic 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.