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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 256523 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
124.1.i.a	$124$	$1$	124.i	124.i	$6$	$4$	$2$	$0.062$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\zeta_{12}^{3}q^{2}-\zeta_{12}q^{3}-q^{4}-\zeta_{12}^{2}q^{5}+\cdots$
133.1.m.a	$133$	$1$	133.m	133.m	$6$	$4$	$2$	$0.066$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{5}q^{5}+\cdots$
148.1.f.a	$148$	$1$	148.f	37.d	$4$	$2$	$1$	$0.074$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+iq^{3}-q^{7}-iq^{11}+(-1-i)q^{17}+\cdots$
171.1.o.a	$171$	$1$	171.o	171.o	$6$	$4$	$2$	$0.085$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$-2$		$1$		$q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{5}+\cdots$
11.2.a.a	$11$	$2$	11.a	1.a	$1$	$1$	$1$	$0.088$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-2$	$-1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots$
201.1.g.a	$201$	$1$	201.g	201.g	$6$	$4$	$2$	$0.100$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{3}q^{3}-\zeta_{12}^{2}q^{6}+\cdots$
13.2.e.a	$13$	$2$	13.e	13.e	$6$	$2$	$1$	$0.104$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-3$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
209.1.h.a	$209$	$1$	209.h	209.h	$6$	$4$	$2$	$0.104$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$-2$	$-2$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{2}q^{3}-\zeta_{12}^{2}q^{5}+\cdots$
219.1.j.b	$219$	$1$	219.j	219.j	$6$	$4$	$2$	$0.109$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{4}q^{6}+\cdots$
14.2.a.a	$14$	$2$	14.a	1.a	$1$	$1$	$1$	$0.112$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$-2$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}+q^{7}-q^{8}+\cdots$
224.1.r.a	$224$	$1$	224.r	28.g	$6$	$4$	$2$	$0.112$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+\zeta_{12}^{5}q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{7}+\cdots$
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		$2$	$0$	$2$	$-2$	$0$	$0$		$1$		$q+(1-i)q^{2}-q^{3}-iq^{4}-iq^{5}+(-1+\cdots)q^{6}+\cdots$
15.2.a.a	$15$	$2$	15.a	1.a	$1$	$1$	$1$	$0.120$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots$
16.2.e.a	$16$	$2$	16.e	16.e	$4$	$2$	$1$	$0.128$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$-2$	$-2$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-i)q^{2}+(-1+i)q^{3}+2iq^{4}+\cdots$
261.1.f.a	$261$	$1$	261.f	29.c	$4$	$4$	$2$	$0.130$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{8}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}-q^{7}+\zeta_{8}^{3}q^{8}+\cdots$
17.2.a.a	$17$	$2$	17.a	1.a	$1$	$1$	$1$	$0.136$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-2q^{5}+4q^{7}+3q^{8}-3q^{9}+\cdots$
17.2.d.a	$17$	$2$	17.d	17.d	$8$	$4$	$1$	$0.136$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$-4$	$-4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots$
273.1.s.b	$273$	$1$	273.s	273.s	$6$	$4$	$2$	$0.136$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\zeta_{12}^{3}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{5}q^{5}+\cdots$
273.1.bm.b	$273$	$1$	273.bm	273.am	$6$	$4$	$2$	$0.136$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{4}q^{6}+\cdots$
283.1.b.b	$283$	$1$	283.b	283.b	$2$	$2$	$2$	$0.141$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\beta q^{2}+\beta q^{3}-q^{4}+\beta q^{5}+2q^{6}+\cdots$
18.2.c.a	$18$	$2$	18.c	9.c	$3$	$2$	$1$	$0.144$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-1$	$-3$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
288.1.o.a	$288$	$1$	288.o	36.f	$6$	$4$	$2$	$0.144$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{5}+\zeta_{12}q^{7}-q^{9}+\cdots$
296.1.k.a	$296$	$1$	296.k	37.d	$4$	$2$	$1$	$0.148$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$-2$	$-2$		$1$		$q-iq^{3}+(-1-i)q^{5}-q^{7}-iq^{11}+\cdots$
301.1.r.a	$301$	$1$	301.r	301.r	$6$	$4$	$2$	$0.150$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}-\zeta_{12}q^{5}-q^{6}+\cdots$
19.2.a.a	$19$	$2$	19.a	1.a	$1$	$1$	$1$	$0.152$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+3q^{11}+\cdots$
19.2.e.a	$19$	$2$	19.e	19.e	$9$	$6$	$1$	$0.152$	$\Q(\zeta_{18})$	$_{}$	None	None		$2$	$0$	$-6$	$-3$	$-6$	$0$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-1+\zeta_{18}-\zeta_{18}^{2})q^{2}+(-1+\zeta_{18}^{2}+\cdots)q^{3}+\cdots$
309.1.h.a	$309$	$1$	309.h	309.h	$6$	$4$	$2$	$0.154$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$-4$	$0$	$2$		$1$		$q-\zeta_{12}q^{2}-q^{3}+\zeta_{12}^{5}q^{5}+\zeta_{12}q^{6}+\cdots$
20.2.a.a	$20$	$2$	20.a	1.a	$1$	$1$	$1$	$0.160$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots$
325.1.u.a	$325$	$1$	325.u	65.q	$12$	$8$	$2$	$0.162$	$\Q(\zeta_{24})$	$A_{4}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{5}q^{2}-\zeta_{24}^{11}q^{3}-\zeta_{24}^{4}q^{6}+\cdots$
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		$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$
21.2.a.a	$21$	$2$	21.a	1.a	$1$	$1$	$1$	$0.168$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$1$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots$
21.2.e.a	$21$	$2$	21.e	7.c	$3$	$2$	$1$	$0.168$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-2$	$-1$	$2$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}-\zeta_{6}q^{3}-2\zeta_{6}q^{4}+\cdots$
344.1.b.a	$344$	$1$	344.b	43.b	$2$	$2$	$2$	$0.172$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{3}-\beta q^{5}+\beta q^{7}-q^{9}-q^{11}+\cdots$
344.1.l.b	$344$	$1$	344.l	344.l	$6$	$4$	$2$	$0.172$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\zeta_{12}^{3}q^{2}-\zeta_{12}^{4}q^{3}-q^{4}-\zeta_{12}q^{5}+\cdots$
22.2.c.a	$22$	$2$	22.c	11.c	$5$	$4$	$1$	$0.176$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$-1$	$-4$	$-6$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots$
23.2.a.a	$23$	$2$	23.a	1.a	$1$	$2$	$2$	$0.184$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
23.2.c.a	$23$	$2$	23.c	23.c	$11$	$10$	$1$	$0.184$	$\Q(\zeta_{22})$	$_{}$	None	None		$2$	$0$	$-7$	$-7$	$-3$	$-5$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(-\zeta_{22}+\zeta_{22}^{4}-\zeta_{22}^{5}+\zeta_{22}^{6}+\cdots)q^{2}+\cdots$
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		$4$	$0$	$0$	$-2$	$2$	$0$		$1$		$q+(-\zeta_{12}^{2}+\zeta_{12}^{5})q^{3}+\zeta_{12}^{2}q^{5}+\cdots$
24.2.a.a	$24$	$2$	24.a	1.a	$1$	$1$	$1$	$0.192$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$
24.2.d.a	$24$	$2$	24.d	8.b	$2$	$2$	$2$	$0.192$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+i)q^{2}+iq^{3}-2iq^{4}-2iq^{5}+\cdots$
399.1.n.a	$399$	$1$	399.n	399.n	$6$	$4$	$2$	$0.199$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{3}q^{5}+\cdots$
399.1.bi.a	$399$	$1$	399.bi	399.ai	$6$	$4$	$2$	$0.199$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{5}q^{5}+\cdots$
25.2.d.a	$25$	$2$	25.d	25.d	$5$	$4$	$1$	$0.200$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$-2$	$-1$	$-5$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots$
25.2.e.a	$25$	$2$	25.e	25.e	$10$	$8$	$2$	$0.200$	8.0.58140625.2	$_{}$	None	None		$2$	$0$	$-5$	$-5$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-1+\beta _{1})q^{2}+(-1+\beta _{2}-\beta _{3}+\beta _{7})q^{3}+\cdots$
403.1.p.a	$403$	$1$	403.p	403.p	$6$	$4$	$2$	$0.201$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$-2$	$0$	$0$	$2$		$1$		$q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{5}q^{3}+\zeta_{12}q^{6}-\zeta_{12}^{4}q^{7}+\cdots$
404.1.f.a	$404$	$1$	404.f	101.c	$4$	$2$	$1$	$0.202$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$-2$	$2$	$2$		$1$		$q+(-1+i)q^{3}+q^{5}+(1-i)q^{7}-iq^{9}+\cdots$

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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.