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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 2924 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
23.1.b.a	$23$	$1$	23.b	23.b	$2$	$1$	$1$	$0.011$	$\Q$	$D_{3}$	$\Q(\sqrt{-23}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-q^{2}-q^{3}+q^{6}+q^{8}-q^{13}-q^{16}+\cdots$
31.1.b.a	$31$	$1$	31.b	31.b	$2$	$1$	$1$	$0.015$	$\Q$	$D_{3}$	$\Q(\sqrt{-31}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$	$1$		$q-q^{2}-q^{5}-q^{7}+q^{8}+q^{9}+q^{10}+\cdots$
44.1.d.a	$44$	$1$	44.d	11.b	$2$	$1$	$1$	$0.022$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$	$1$		$q-q^{3}-q^{5}+q^{11}+q^{15}-q^{23}+q^{27}+\cdots$
52.1.j.a	$52$	$1$	52.j	52.j	$6$	$2$	$1$	$0.026$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
57.1.h.a	$57$	$1$	57.h	57.h	$6$	$2$	$1$	$0.028$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{7}-\zeta_{6}q^{9}+q^{12}+\cdots$
59.1.b.a	$59$	$1$	59.b	59.b	$2$	$1$	$1$	$0.029$	$\Q$	$D_{3}$	$\Q(\sqrt{-59}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q-q^{3}+q^{4}-q^{5}-q^{7}-q^{12}+q^{15}+\cdots$
72.1.p.a	$72$	$1$	72.p	72.p	$6$	$2$	$1$	$0.036$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots$
76.1.c.a	$76$	$1$	76.c	19.b	$2$	$1$	$1$	$0.038$	$\Q$	$D_{3}$	$\Q(\sqrt{-19}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$-1$	$1$		$q-q^{5}-q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots$
83.1.b.a	$83$	$1$	83.b	83.b	$2$	$1$	$1$	$0.041$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q-q^{3}+q^{4}-q^{7}-q^{11}-q^{12}+q^{16}+\cdots$
84.1.p.a	$84$	$1$	84.p	21.h	$6$	$2$	$1$	$0.042$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}-q^{13}+\cdots$
87.1.d.a	$87$	$1$	87.d	87.d	$2$	$1$	$1$	$0.043$	$\Q$	$D_{3}$	$\Q(\sqrt{-87}) $	None	✓	$2$	$0$	$-1$	$1$	$0$	$-1$	$1$		$q-q^{2}+q^{3}-q^{6}-q^{7}+q^{8}+q^{9}+\cdots$
87.1.d.b	$87$	$1$	87.d	87.d	$2$	$1$	$1$	$0.043$	$\Q$	$D_{3}$	$\Q(\sqrt{-87}) $	None	✓	$2$	$0$	$1$	$-1$	$0$	$-1$	$1$		$q+q^{2}-q^{3}-q^{6}-q^{7}-q^{8}+q^{9}+\cdots$
99.1.h.a	$99$	$1$	99.h	99.h	$6$	$2$	$1$	$0.049$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-1$	$1$	$0$	$1$		$q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+\cdots$
104.1.h.a	$104$	$1$	104.h	104.h	$2$	$1$	$1$	$0.052$	$\Q$	$D_{3}$	$\Q(\sqrt{-26}) $	None	✓	$2$	$0$	$-1$	$-1$	$1$	$1$	$1$		$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
104.1.h.b	$104$	$1$	104.h	104.h	$2$	$1$	$1$	$0.052$	$\Q$	$D_{3}$	$\Q(\sqrt{-26}) $	None	✓	$2$	$0$	$1$	$-1$	$-1$	$-1$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
107.1.b.a	$107$	$1$	107.b	107.b	$2$	$1$	$1$	$0.053$	$\Q$	$D_{3}$	$\Q(\sqrt{-107}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{4}-q^{11}-q^{12}-q^{13}+q^{16}+\cdots$
108.1.c.a	$108$	$1$	108.c	3.b	$2$	$1$	$1$	$0.054$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-1$	$1$		$q-q^{7}-q^{13}-q^{19}+q^{25}+2q^{31}+\cdots$
111.1.i.a	$111$	$1$	111.i	111.i	$6$	$2$	$1$	$0.055$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$1$	$1$		$q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
116.1.d.a	$116$	$1$	116.d	116.d	$2$	$1$	$1$	$0.058$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$-1$	$1$	$-1$	$0$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
116.1.d.b	$116$	$1$	116.d	116.d	$2$	$1$	$1$	$0.058$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$1$	$-1$	$-1$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
133.1.r.a	$133$	$1$	133.r	133.r	$6$	$2$	$1$	$0.066$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$1$	$-1$	$1$		$q-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
135.1.d.a	$135$	$1$	135.d	15.d	$2$	$1$	$1$	$0.067$	$\Q$	$D_{3}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$0$	$1$		$q-q^{2}+q^{5}+q^{8}-q^{10}-q^{16}-q^{17}+\cdots$
135.1.d.b	$135$	$1$	135.d	15.d	$2$	$1$	$1$	$0.067$	$\Q$	$D_{3}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$0$	$1$		$q+q^{2}-q^{5}-q^{8}-q^{10}-q^{16}+q^{17}+\cdots$
139.1.b.a	$139$	$1$	139.b	139.b	$2$	$1$	$1$	$0.069$	$\Q$	$D_{3}$	$\Q(\sqrt{-139}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$-1$	$1$		$q+q^{4}-q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
140.1.h.a	$140$	$1$	140.h	35.c	$2$	$1$	$1$	$0.070$	$\Q$	$D_{3}$	$\Q(\sqrt{-35}) $	None	✓	$2$	$0$	$0$	$-1$	$1$	$1$	$1$		$q-q^{3}+q^{5}+q^{7}-q^{11}-q^{13}-q^{15}+\cdots$
140.1.h.b	$140$	$1$	140.h	35.c	$2$	$1$	$1$	$0.070$	$\Q$	$D_{3}$	$\Q(\sqrt{-35}) $	None	✓	$2$	$0$	$0$	$1$	$-1$	$-1$	$1$		$q+q^{3}-q^{5}-q^{7}-q^{11}+q^{13}-q^{15}+\cdots$
140.1.p.a	$140$	$1$	140.p	140.p	$6$	$2$	$1$	$0.070$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$1$	$-1$	$-1$	$1$		$q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots$
140.1.p.b	$140$	$1$	140.p	140.p	$6$	$2$	$1$	$0.070$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$-1$	$-1$	$1$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots$
148.1.i.a	$148$	$1$	148.i	148.i	$6$	$2$	$1$	$0.074$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
152.1.g.a	$152$	$1$	152.g	152.g	$2$	$1$	$1$	$0.076$	$\Q$	$D_{3}$	$\Q(\sqrt{-38}) $	None	✓	$2$	$0$	$-1$	$1$	$0$	$-1$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
152.1.g.b	$152$	$1$	152.g	152.g	$2$	$1$	$1$	$0.076$	$\Q$	$D_{3}$	$\Q(\sqrt{-38}) $	None	✓	$2$	$0$	$1$	$-1$	$0$	$-1$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots$
152.1.k.a	$152$	$1$	152.k	152.k	$6$	$2$	$1$	$0.076$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots$
156.1.o.a	$156$	$1$	156.o	39.i	$6$	$2$	$1$	$0.078$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$1$	$1$		$q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{13}+\cdots$
168.1.s.a	$168$	$1$	168.s	168.s	$6$	$2$	$1$	$0.084$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$-1$	$-1$	$1$	$-1$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$
168.1.s.b	$168$	$1$	168.s	168.s	$6$	$2$	$1$	$0.084$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$1$	$1$	$-1$	$-1$	$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\cdots$
172.1.b.a	$172$	$1$	172.b	43.b	$2$	$1$	$1$	$0.086$	$\Q$	$D_{3}$	$\Q(\sqrt{-43}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}-q^{11}-q^{13}-q^{17}-q^{23}+\cdots$
175.1.c.a	$175$	$1$	175.c	35.c	$2$	$2$	$2$	$0.087$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}+iq^{7}-iq^{8}-q^{9}-q^{11}+\cdots$
175.1.d.a	$175$	$1$	175.d	7.b	$2$	$1$	$1$	$0.087$	$\Q$	$D_{3}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$1$	$1$		$q-q^{2}+q^{7}+q^{8}+q^{9}-q^{11}-q^{14}+\cdots$
175.1.d.b	$175$	$1$	175.d	7.b	$2$	$1$	$1$	$0.087$	$\Q$	$D_{3}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$-1$	$1$		$q+q^{2}-q^{7}-q^{8}+q^{9}-q^{11}-q^{14}+\cdots$
176.1.h.a	$176$	$1$	176.h	11.b	$2$	$1$	$1$	$0.088$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$1$	$-1$	$0$	$1$		$q+q^{3}-q^{5}-q^{11}-q^{15}+q^{23}-q^{27}+\cdots$
180.1.p.a	$180$	$1$	180.p	180.p	$6$	$2$	$1$	$0.090$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$-1$	$-1$	$1$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$
180.1.p.b	$180$	$1$	180.p	180.p	$6$	$2$	$1$	$0.090$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$1$	$-1$	$-1$	$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$
189.1.q.a	$189$	$1$	189.q	21.h	$6$	$2$	$1$	$0.094$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+\zeta_{6}^{2}q^{4}+q^{7}-q^{13}-\zeta_{6}q^{16}-\zeta_{6}q^{19}+\cdots$
199.1.b.a	$199$	$1$	199.b	199.b	$2$	$1$	$1$	$0.099$	$\Q$	$D_{3}$	$\Q(\sqrt{-199}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$2$	$1$		$q-q^{2}-q^{5}+2q^{7}+q^{8}+q^{9}+q^{10}+\cdots$
200.1.e.a	$200$	$1$	200.e	40.e	$2$	$2$	$2$	$0.100$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{8}-q^{11}+\cdots$
200.1.g.a	$200$	$1$	200.g	8.d	$2$	$1$	$1$	$0.100$	$\Q$	$D_{3}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-q^{11}+\cdots$
200.1.g.b	$200$	$1$	200.g	8.d	$2$	$1$	$1$	$0.100$	$\Q$	$D_{3}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-q^{11}+\cdots$
204.1.g.a	$204$	$1$	204.g	51.c	$2$	$1$	$1$	$0.102$	$\Q$	$D_{3}$	$\Q(\sqrt{-51}) $	None	✓	$2$	$0$	$0$	$-1$	$1$	$0$	$1$		$q-q^{3}+q^{5}+q^{9}+q^{11}-q^{13}-q^{15}+\cdots$
204.1.g.b	$204$	$1$	204.g	51.c	$2$	$1$	$1$	$0.102$	$\Q$	$D_{3}$	$\Q(\sqrt{-51}) $	None	✓	$2$	$0$	$0$	$1$	$-1$	$0$	$1$		$q+q^{3}-q^{5}+q^{9}-q^{11}-q^{13}-q^{15}+\cdots$
207.1.d.a	$207$	$1$	207.d	23.b	$2$	$1$	$1$	$0.103$	$\Q$	$D_{3}$	$\Q(\sqrt{-23}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}-q^{8}-q^{13}-q^{16}-q^{23}+q^{25}+\cdots$

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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.