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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 59 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				A-L signs				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	7	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5082.2.a.a	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$-4$	$-1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-q^{7}+\cdots$
5082.2.a.b	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$-4$	$1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}+q^{7}+\cdots$
5082.2.a.c	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$2$	$-1$	$-1$	$-3$	$-1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots$
5082.2.a.d	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$-2$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots$
5082.2.a.e	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$0$	$-1$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots$
5082.2.a.f	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$1$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
5082.2.a.g	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$2$	$-1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots$
5082.2.a.h	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$2$	$-1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots$
5082.2.a.i	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$4$	$1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+4q^{5}+q^{6}+q^{7}+\cdots$
5082.2.a.j	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$-3$	$-1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots$
5082.2.a.k	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$-2$	$1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots$
5082.2.a.l	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$0$	$-1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
5082.2.a.m	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$2$	$1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots$
5082.2.a.n	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$2$	$1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots$
5082.2.a.o	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$-4$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-q^{7}+\cdots$
5082.2.a.p	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$-3$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{7}+\cdots$
5082.2.a.q	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$-2$	$-1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots$
5082.2.a.r	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$0$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
5082.2.a.s	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
5082.2.a.t	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$1$	$-1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
5082.2.a.u	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$2$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots$
5082.2.a.v	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$2$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots$
5082.2.a.w	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$2$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots$
5082.2.a.x	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$4$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}-q^{7}+\cdots$
5082.2.a.y	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-3$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{7}+\cdots$
5082.2.a.z	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-2$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-q^{7}+\cdots$
5082.2.a.ba	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$0$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots$
5082.2.a.bb	$5082$	$2$	5082.a	1.a	$1$	$1$	$1$	$40.580$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$2$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots$
5082.2.a.bc	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$-2$	$-2$	$-4$	$2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots$
5082.2.a.bd	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$-2$	$-3$	$-2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots$
5082.2.a.be	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$-2$	$-2$	$0$	$-2$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{7}+\cdots$
5082.2.a.bf	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$-2$	$1$	$2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}+q^{7}+\cdots$
5082.2.a.bg	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$-2$	$-2$	$4$	$2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(2+\beta )q^{5}+q^{6}+\cdots$
5082.2.a.bh	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$2$	$-5$	$-2$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-2-\beta )q^{5}-q^{6}+\cdots$
5082.2.a.bi	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$-2$	$2$	$-4$	$2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}-q^{6}+\cdots$
5082.2.a.bj	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$2$	$-1$	$2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}+q^{7}+\cdots$
5082.2.a.bk	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$2$	$2$	$-2$	$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots$
5082.2.a.bl	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{33}) $	None	✓	$1$	$0$	$-2$	$2$	$3$	$2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots$
5082.2.a.bm	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$-2$	$-4$	$-2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots$
5082.2.a.bn	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-2$	$-3$	$2$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots$
5082.2.a.bo	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$2$	$-2$	$0$	$2$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}+q^{7}+\cdots$
5082.2.a.bp	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-2$	$1$	$-2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{7}+\cdots$
5082.2.a.bq	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$-2$	$4$	$-2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(2+\beta )q^{5}-q^{6}+\cdots$
5082.2.a.br	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$2$	$-5$	$2$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-2-\beta )q^{5}+q^{6}+\cdots$
5082.2.a.bs	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$2$	$2$	$-4$	$-2$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}+q^{6}+\cdots$
5082.2.a.bt	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$2$	$-1$	$-2$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-\beta q^{5}+q^{6}-q^{7}+\cdots$
5082.2.a.bu	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$2$	$0$	$-2$	$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{7}+\cdots$
5082.2.a.bv	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$2$	$2$	$2$	$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots$
5082.2.a.bw	$5082$	$2$	5082.a	1.a	$1$	$2$	$2$	$40.580$	$\Q(\sqrt{33}) $	None	✓	$1$	$0$	$2$	$2$	$3$	$-2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots$
5082.2.a.bx	$5082$	$2$	5082.a	1.a	$1$	$4$	$4$	$40.580$	4.4.8000.1	None	✓	$1$	$1$	$-4$	$-4$	$2$	$4$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots$

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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.