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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 8037 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4002.2.a.a	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$2$	$-1$	$-1$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-2q^{7}+\cdots$
4002.2.a.b	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-4q^{7}-q^{8}+\cdots$
4002.2.a.c	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots$
4002.2.a.d	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-3q^{7}+\cdots$
4002.2.a.e	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
4002.2.a.f	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots$
4002.2.a.g	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{8}+\cdots$
4002.2.a.h	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots$
4002.2.a.i	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+2q^{7}+\cdots$
4002.2.a.j	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots$
4002.2.a.k	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
4002.2.a.l	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+4q^{7}+\cdots$
4002.2.a.m	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-4q^{7}+\cdots$
4002.2.a.n	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-4q^{7}+\cdots$
4002.2.a.o	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-3q^{7}+\cdots$
4002.2.a.p	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
4002.2.a.q	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots$
4002.2.a.r	$4002$	$2$	4002.a	1.a	$1$	$1$	$1$	$31.956$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{7}+\cdots$
4004.2.a.a	$4004$	$2$	4004.a	1.a	$1$	$1$	$1$	$31.972$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{7}+q^{9}-q^{11}+q^{13}+6q^{17}+\cdots$
4004.2.a.b	$4004$	$2$	4004.a	1.a	$1$	$1$	$1$	$31.972$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}-q^{7}-2q^{9}-q^{11}+q^{13}+\cdots$
4004.2.a.c	$4004$	$2$	4004.a	1.a	$1$	$1$	$1$	$31.972$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+4q^{5}+q^{7}+q^{9}+q^{11}-q^{13}+\cdots$
4005.2.a.a	$4005$	$2$	4005.a	1.a	$1$	$1$	$1$	$31.980$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}+4q^{7}+3q^{8}-q^{10}+\cdots$
4005.2.a.b	$4005$	$2$	4005.a	1.a	$1$	$1$	$1$	$31.980$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{5}-4q^{7}-2q^{11}+4q^{13}+\cdots$
4005.2.a.c	$4005$	$2$	4005.a	1.a	$1$	$1$	$1$	$31.980$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{5}-4q^{7}+2q^{11}+4q^{13}+\cdots$
4005.2.a.d	$4005$	$2$	4005.a	1.a	$1$	$1$	$1$	$31.980$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}-4q^{11}+\cdots$
4006.2.a.a	$4006$	$2$	4006.a	1.a	$1$	$1$	$1$	$31.988$	$\Q$	None	✓	$1$	$2$	$-1$	$0$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{5}-2q^{7}-q^{8}-3q^{9}+\cdots$
4006.2.a.b	$4006$	$2$	4006.a	1.a	$1$	$1$	$1$	$31.988$	$\Q$	None	✓	$1$	$2$	$1$	$-2$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-3q^{5}-2q^{6}-2q^{7}+\cdots$
4006.2.a.c	$4006$	$2$	4006.a	1.a	$1$	$1$	$1$	$31.988$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots$
4008.2.a.a	$4008$	$2$	4008.a	1.a	$1$	$1$	$1$	$32.004$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-3q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
4008.2.a.b	$4008$	$2$	4008.a	1.a	$1$	$1$	$1$	$32.004$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
4008.2.a.c	$4008$	$2$	4008.a	1.a	$1$	$1$	$1$	$32.004$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}+2q^{17}-8q^{19}-4q^{23}+\cdots$
4008.2.a.d	$4008$	$2$	4008.a	1.a	$1$	$1$	$1$	$32.004$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
4009.2.a.a	$4009$	$2$	4009.a	1.a	$1$	$1$	$1$	$32.012$	$\Q$	None	✓	$1$	$0$	$-1$	$2$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}-q^{4}+3q^{5}-2q^{6}+3q^{8}+\cdots$
4010.2.a.a	$4010$	$2$	4010.a	1.a	$1$	$1$	$1$	$32.020$	$\Q$	None	✓	$1$	$0$	$-1$	$-2$	$1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-4q^{7}+\cdots$
4010.2.a.b	$4010$	$2$	4010.a	1.a	$1$	$1$	$1$	$32.020$	$\Q$	None	✓	$1$	$1$	$-1$	$2$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-q^{5}-2q^{6}-q^{8}+\cdots$
4010.2.a.c	$4010$	$2$	4010.a	1.a	$1$	$1$	$1$	$32.020$	$\Q$	None	✓	$1$	$1$	$-1$	$2$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}+q^{5}-2q^{6}-q^{8}+\cdots$
4010.2.a.d	$4010$	$2$	4010.a	1.a	$1$	$1$	$1$	$32.020$	$\Q$	None	✓	$1$	$0$	$-1$	$3$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots$
4010.2.a.e	$4010$	$2$	4010.a	1.a	$1$	$1$	$1$	$32.020$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots$
4010.2.a.f	$4010$	$2$	4010.a	1.a	$1$	$1$	$1$	$32.020$	$\Q$	None	✓	$1$	$0$	$1$	$2$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}+4q^{7}+\cdots$
4011.2.a.a	$4011$	$2$	4011.a	1.a	$1$	$1$	$1$	$32.028$	$\Q$	None	✓	$1$	$0$	$-2$	$1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+q^{7}+\cdots$
4011.2.a.b	$4011$	$2$	4011.a	1.a	$1$	$1$	$1$	$32.028$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
4011.2.a.c	$4011$	$2$	4011.a	1.a	$1$	$1$	$1$	$32.028$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-4$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-4q^{5}-q^{7}+q^{9}-3q^{11}+\cdots$
4011.2.a.d	$4011$	$2$	4011.a	1.a	$1$	$1$	$1$	$32.028$	$\Q$	None	✓	$1$	$0$	$2$	$-1$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}+4q^{5}-2q^{6}+\cdots$
4012.2.a.a	$4012$	$2$	4012.a	1.a	$1$	$1$	$1$	$32.036$	$\Q$	None	✓	$1$	$2$	$0$	$-3$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-3q^{5}-q^{7}+6q^{9}-2q^{11}+\cdots$
4012.2.a.b	$4012$	$2$	4012.a	1.a	$1$	$1$	$1$	$32.036$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$-1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}-5q^{7}+6q^{9}-2q^{11}+\cdots$
4012.2.a.c	$4012$	$2$	4012.a	1.a	$1$	$1$	$1$	$32.036$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}+q^{7}-2q^{9}+2q^{11}+\cdots$
4013.2.a.a	$4013$	$2$	4013.a	1.a	$1$	$1$	$1$	$32.044$	$\Q$	None	✓	$1$	$0$	$2$	$-2$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-2q^{3}+2q^{4}+4q^{5}-4q^{6}+\cdots$
4014.2.a.a	$4014$	$2$	4014.a	1.a	$1$	$1$	$1$	$32.052$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}+2q^{11}+\cdots$
4014.2.a.b	$4014$	$2$	4014.a	1.a	$1$	$1$	$1$	$32.052$	$\Q$	None	✓	$1$	$2$	$-1$	$0$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots$
4014.2.a.c	$4014$	$2$	4014.a	1.a	$1$	$1$	$1$	$32.052$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}+2q^{11}+4q^{13}+\cdots$

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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.