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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 30268 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
4001.2.a.a	$4001$	$2$	4001.a	1.a	$1$	$149$	$149$	$31.948$		None	✓	$1$	$1$	$-6$	$-28$	$-19$	$-47$	$+$		$\mathrm{SU}(2)$
4001.2.a.b	$4001$	$2$	4001.a	1.a	$1$	$184$	$184$	$31.948$		None	✓	$1$	$0$	$3$	$28$	$15$	$49$	$-$		$\mathrm{SU}(2)$
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	✓	$1$	$0$	$1$	$1$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{7}+\cdots$
4002.2.a.s	$4002$	$2$	4002.a	1.a	$1$	$2$	$2$	$31.956$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$-2$	$-2$	$-3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots$
4002.2.a.t	$4002$	$2$	4002.a	1.a	$1$	$2$	$2$	$31.956$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2\beta q^{5}+q^{6}+\beta q^{7}+\cdots$
4002.2.a.u	$4002$	$2$	4002.a	1.a	$1$	$2$	$2$	$31.956$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$-2$	$2$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+\beta q^{7}+\cdots$
4002.2.a.v	$4002$	$2$	4002.a	1.a	$1$	$2$	$2$	$31.956$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$2$	$-2$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots$
4002.2.a.w	$4002$	$2$	4002.a	1.a	$1$	$2$	$2$	$31.956$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$2$	$6$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+3q^{7}+\cdots$
4002.2.a.x	$4002$	$2$	4002.a	1.a	$1$	$2$	$2$	$31.956$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$2$	$2$	$8$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+(2-\beta )q^{7}+\cdots$
4002.2.a.y	$4002$	$2$	4002.a	1.a	$1$	$3$	$3$	$31.956$	3.3.1772.1	None	✓	$1$	$0$	$-3$	$-3$	$-1$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}+(2+\cdots)q^{7}+\cdots$
4002.2.a.z	$4002$	$2$	4002.a	1.a	$1$	$3$	$3$	$31.956$	3.3.316.1	None	✓	$1$	$1$	$3$	$-3$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots$
4002.2.a.ba	$4002$	$2$	4002.a	1.a	$1$	$4$	$4$	$31.956$	4.4.16448.2	None	✓	$1$	$0$	$-4$	$-4$	$2$	$6$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta _{3}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots$
4002.2.a.bb	$4002$	$2$	4002.a	1.a	$1$	$4$	$4$	$31.956$	4.4.23252.1	None	✓	$1$	$1$	$-4$	$4$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-1+\beta _{3})q^{5}-q^{6}+\cdots$
4002.2.a.bc	$4002$	$2$	4002.a	1.a	$1$	$4$	$4$	$31.956$	4.4.11324.1	None	✓	$1$	$1$	$4$	$4$	$-4$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots$
4002.2.a.bd	$4002$	$2$	4002.a	1.a	$1$	$4$	$4$	$31.956$	4.4.19796.1	None	✓	$1$	$0$	$4$	$4$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-\beta _{3}q^{5}+q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots$
4002.2.a.be	$4002$	$2$	4002.a	1.a	$1$	$5$	$5$	$31.956$	5.5.2389280.1	None	✓	$1$	$1$	$-5$	$-5$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta _{2}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
4002.2.a.bf	$4002$	$2$	4002.a	1.a	$1$	$6$	$6$	$31.956$	6.6.61157024.1	None	✓	$1$	$0$	$-6$	$6$	$3$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+\beta _{4}q^{5}-q^{6}+(\beta _{4}+\cdots)q^{7}+\cdots$
4002.2.a.bg	$4002$	$2$	4002.a	1.a	$1$	$7$	$7$	$31.956$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$-7$	$-7$	$2$	$-5$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-\beta _{5}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
4002.2.a.bh	$4002$	$2$	4002.a	1.a	$1$	$7$	$7$	$31.956$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$7$	$7$	$1$	$-2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+\beta _{3}q^{5}+q^{6}-\beta _{6}q^{7}+\cdots$
4002.2.a.bi	$4002$	$2$	4002.a	1.a	$1$	$8$	$8$	$31.956$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-8$	$8$	$-3$	$-6$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-\beta _{4}q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
4002.2.a.bj	$4002$	$2$	4002.a	1.a	$1$	$8$	$8$	$31.956$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$8$	$-8$	$1$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-\beta _{4}q^{7}+\cdots$
4002.2.a.bk	$4002$	$2$	4002.a	1.a	$1$	$8$	$8$	$31.956$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$8$	$-8$	$2$	$5$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots$
4003.2.a.a	$4003$	$2$	4003.a	1.a	$1$	$2$	$2$	$31.964$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+\beta q^{3}+\beta q^{5}+2q^{6}-q^{7}+\cdots$
4003.2.a.b	$4003$	$2$	4003.a	1.a	$1$	$152$	$152$	$31.964$		None	✓	$1$	$1$	$-22$	$-18$	$-59$	$-19$	$+$		$\mathrm{SU}(2)$
4003.2.a.c	$4003$	$2$	4003.a	1.a	$1$	$179$	$179$	$31.964$		None	✓	$1$	$0$	$22$	$16$	$61$	$21$	$-$		$\mathrm{SU}(2)$
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	✓	$1$	$0$	$0$	$2$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+4q^{5}+q^{7}+q^{9}+q^{11}-q^{13}+\cdots$
4004.2.a.d	$4004$	$2$	4004.a	1.a	$1$	$4$	$4$	$31.972$	4.4.3981.1	None	✓	$1$	$1$	$0$	$-3$	$-1$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{3})q^{3}+(\beta _{2}+\beta _{3})q^{5}+q^{7}+\cdots$
4004.2.a.e	$4004$	$2$	4004.a	1.a	$1$	$4$	$4$	$31.972$	$\Q(\zeta_{15})^+$	None	✓	$1$	$1$	$0$	$1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+\cdots$
4004.2.a.f	$4004$	$2$	4004.a	1.a	$1$	$5$	$5$	$31.972$	5.5.463341.1	None	✓	$1$	$1$	$0$	$3$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}-\beta _{2}q^{5}-q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
4004.2.a.g	$4004$	$2$	4004.a	1.a	$1$	$6$	$6$	$31.972$	6.6.246302029.1	None	✓	$1$	$1$	$0$	$-2$	$-3$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{4})q^{5}+q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots$
4004.2.a.h	$4004$	$2$	4004.a	1.a	$1$	$9$	$9$	$31.972$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$0$	$3$	$0$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{4}q^{5}+q^{7}+(2+\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$

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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.