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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 4023 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
18.2.c.a	$18$	$2$	18.c	9.c	$3$	$2$	$1$	$0.144$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$-3$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
21.2.e.a	$21$	$2$	21.e	7.c	$3$	$2$	$1$	$0.168$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-2$	$-1$	$2$	$-5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}-\zeta_{6}q^{3}-2\zeta_{6}q^{4}+\cdots$
26.2.c.a	$26$	$2$	26.c	13.c	$3$	$2$	$1$	$0.208$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$-2$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}-4\zeta_{6}q^{7}+\cdots$
28.2.e.a	$28$	$2$	28.e	7.c	$3$	$2$	$1$	$0.224$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$-1$	$-3$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{3}+(-3+3\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$
36.2.e.a	$36$	$2$	36.e	9.c	$3$	$2$	$1$	$0.287$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$0$	$-3$	$1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-2\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+\zeta_{6}q^{7}+\cdots$
37.2.c.a	$37$	$2$	37.c	37.c	$3$	$2$	$1$	$0.295$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$-1$	$-2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}-2\zeta_{6}q^{7}+\cdots$
38.2.c.a	$38$	$2$	38.c	19.c	$3$	$2$	$1$	$0.303$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-1$	$0$	$-8$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
39.2.e.a	$39$	$2$	39.e	13.c	$3$	$2$	$1$	$0.311$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$1$	$-2$	$-2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
42.2.e.a	$42$	$2$	42.e	7.c	$3$	$2$	$1$	$0.335$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$1$	$-1$	$1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+(-1+\cdots)q^{5}+\cdots$
42.2.e.b	$42$	$2$	42.e	7.c	$3$	$2$	$1$	$0.335$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-1$	$-3$	$5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+(-3+\cdots)q^{5}+\cdots$
43.2.c.a	$43$	$2$	43.c	43.c	$3$	$2$	$1$	$0.343$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$-1$	$1$	$-3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-1+\zeta_{6})q^{3}-q^{4}+(1-\zeta_{6})q^{5}+\cdots$
45.2.e.a	$45$	$2$	45.e	9.c	$3$	$2$	$1$	$0.359$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$-3$	$1$	$3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
49.2.c.a	$49$	$2$	49.c	7.c	$3$	$2$	$1$	$0.391$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-7}) $		$4$	$0$	$-1$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{3}]$	$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-3q^{8}+3\zeta_{6}q^{9}+\cdots$
7.4.c.a	$7$	$4$	7.c	7.c	$3$	$2$	$1$	$0.413$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-2$	$-7$	$-7$	$28$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}-7\zeta_{6}q^{3}+4\zeta_{6}q^{4}+\cdots$
52.2.e.a	$52$	$2$	52.e	13.c	$3$	$2$	$1$	$0.415$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$-3$	$4$	$-1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\zeta_{6})q^{3}+2q^{5}-\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots$
52.2.e.b	$52$	$2$	52.e	13.c	$3$	$2$	$1$	$0.415$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$2$	$-6$	$4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}-3q^{5}+4\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
54.2.c.a	$54$	$2$	54.c	9.c	$3$	$2$	$1$	$0.431$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$0$	$-2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{7}+\cdots$
56.2.i.a	$56$	$2$	56.i	7.c	$3$	$2$	$1$	$0.447$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$-3$	$1$	$4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-3\zeta_{6}q^{3}+(1-\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots$
56.2.i.b	$56$	$2$	56.i	7.c	$3$	$2$	$1$	$0.447$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$1$	$1$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{3}+(1-\zeta_{6})q^{5}+(-3+2\zeta_{6})q^{7}+\cdots$
57.2.e.a	$57$	$2$	57.e	19.c	$3$	$2$	$1$	$0.455$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$1$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
62.2.c.a	$62$	$2$	62.c	31.c	$3$	$2$	$1$	$0.495$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-2$	$-1$	$3$	$1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+3\zeta_{6}q^{5}+\cdots$
62.2.c.b	$62$	$2$	62.c	31.c	$3$	$2$	$1$	$0.495$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$-3$	$-1$	$3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-3+3\zeta_{6})q^{3}+q^{4}-\zeta_{6}q^{5}+\cdots$
63.2.e.a	$63$	$2$	63.e	7.c	$3$	$2$	$1$	$0.503$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$0$	$0$	$-1$	$1$	$\mathrm{U}(1)[D_{3}]$	$q+2\zeta_{6}q^{4}+(1-3\zeta_{6})q^{7}-7q^{13}+(-4+\cdots)q^{16}+\cdots$
63.2.e.b	$63$	$2$	63.e	7.c	$3$	$2$	$1$	$0.503$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$0$	$-2$	$-5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{5}+\cdots$
63.2.g.a	$63$	$2$	63.g	63.g	$3$	$2$	$1$	$0.503$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$-3$	$-2$	$1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
63.2.h.a	$63$	$2$	63.h	63.h	$3$	$2$	$1$	$0.503$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$0$	$1$	$4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+\zeta_{6}q^{5}+\cdots$
70.2.e.a	$70$	$2$	70.e	7.c	$3$	$2$	$1$	$0.559$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$-3$	$1$	$1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
70.2.e.b	$70$	$2$	70.e	7.c	$3$	$2$	$1$	$0.559$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$2$	$1$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
70.2.e.c	$70$	$2$	70.e	7.c	$3$	$2$	$1$	$0.559$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-1$	$1$	$-1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
70.2.e.d	$70$	$2$	70.e	7.c	$3$	$2$	$1$	$0.559$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$2$	$-1$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
72.2.i.a	$72$	$2$	72.i	9.c	$3$	$2$	$1$	$0.575$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$0$	$1$	$3$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+3\zeta_{6}q^{7}+\cdots$
74.2.c.a	$74$	$2$	74.c	37.c	$3$	$2$	$1$	$0.591$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-2$	$1$	$0$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-2\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots$
74.2.c.b	$74$	$2$	74.c	37.c	$3$	$2$	$1$	$0.591$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$2$	$-3$	$4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+2\zeta_{6}q^{3}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots$
76.2.e.a	$76$	$2$	76.e	19.c	$3$	$2$	$1$	$0.607$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$1$	$1$	$0$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots$
78.2.e.a	$78$	$2$	78.e	13.c	$3$	$2$	$1$	$0.623$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-1$	$6$	$-2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
78.2.e.b	$78$	$2$	78.e	13.c	$3$	$2$	$1$	$0.623$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$1$	$-2$	$2$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
81.2.c.a	$81$	$2$	81.c	9.c	$3$	$2$	$1$	$0.647$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$0$	$0$	$1$	$1$	$\mathrm{U}(1)[D_{3}]$	$q+2\zeta_{6}q^{4}+(1-\zeta_{6})q^{7}-5\zeta_{6}q^{13}+\cdots$
84.2.i.a	$84$	$2$	84.i	7.c	$3$	$2$	$1$	$0.671$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$1$	$2$	$1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{3}+(2-2\zeta_{6})q^{5}+(-1+3\zeta_{6})q^{7}+\cdots$
86.2.c.a	$86$	$2$	86.c	43.c	$3$	$2$	$1$	$0.687$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-2$	$-1$	$-3$	$1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+(-3+3\zeta_{6})q^{5}+\cdots$
90.2.e.a	$90$	$2$	90.e	9.c	$3$	$2$	$1$	$0.719$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$3$	$1$	$1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
90.2.e.b	$90$	$2$	90.e	9.c	$3$	$2$	$1$	$0.719$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-3$	$-1$	$4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
91.2.e.a	$91$	$2$	91.e	7.c	$3$	$2$	$1$	$0.727$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$0$	$1$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots$
91.2.g.a	$91$	$2$	91.g	91.g	$3$	$2$	$1$	$0.727$	$\Q(\sqrt{-3}) $	None		$2$	$1$	$-1$	$-6$	$-3$	$-5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}-3q^{3}+(1-\zeta_{6})q^{4}+(-3+\cdots)q^{5}+\cdots$
91.2.h.a	$91$	$2$	91.h	91.h	$3$	$2$	$1$	$0.727$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$3$	$-3$	$4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+3\zeta_{6}q^{3}-q^{4}-3\zeta_{6}q^{5}+3\zeta_{6}q^{6}+\cdots$
95.2.e.a	$95$	$2$	95.e	19.c	$3$	$2$	$1$	$0.759$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$2$	$1$	$-8$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots$
13.4.c.a	$13$	$4$	13.c	13.c	$3$	$2$	$1$	$0.767$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-4$	$-2$	$34$	$-20$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-4+4\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\cdots$
98.2.c.a	$98$	$2$	98.c	7.c	$3$	$2$	$1$	$0.783$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-2$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
98.2.c.b	$98$	$2$	98.c	7.c	$3$	$2$	$1$	$0.783$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$2$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
99.2.e.a	$99$	$2$	99.e	9.c	$3$	$2$	$1$	$0.791$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$-3$	$-1$	$-4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
99.2.e.b	$99$	$2$	99.e	9.c	$3$	$2$	$1$	$0.791$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$-3$	$3$	$4$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\zeta_{6})q^{3}+2\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots$

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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.