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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 92 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	5	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6050.2.a.a	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$-3$	$0$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}+q^{4}+3q^{6}+q^{7}-q^{8}+\cdots$
6050.2.a.b	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$-3$	$0$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}+q^{4}+3q^{6}+q^{7}-q^{8}+\cdots$
6050.2.a.c	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$-1$	$-2$	$0$	$-3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}-3q^{7}-q^{8}+\cdots$
6050.2.a.d	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$-2$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots$
6050.2.a.e	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$-2$	$0$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}+q^{7}-q^{8}+\cdots$
6050.2.a.f	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$0$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-3q^{7}-q^{8}+\cdots$
6050.2.a.g	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$0$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots$
6050.2.a.h	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$0$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots$
6050.2.a.i	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$0$	$5$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+5q^{7}-q^{8}+\cdots$
6050.2.a.j	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}-3q^{9}+q^{13}+\cdots$
6050.2.a.k	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$-2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}-3q^{9}+q^{13}+\cdots$
6050.2.a.l	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$0$	$3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+3q^{7}-q^{8}+\cdots$
6050.2.a.m	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$0$	$3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+3q^{7}-q^{8}+\cdots$
6050.2.a.n	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$-1$	$2$	$0$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-4q^{7}-q^{8}+\cdots$
6050.2.a.o	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$2$	$0$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-3q^{7}-q^{8}+\cdots$
6050.2.a.p	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots$
6050.2.a.q	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots$
6050.2.a.r	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$-1$	$2$	$0$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}+q^{7}-q^{8}+\cdots$
6050.2.a.s	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$-1$	$2$	$0$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}+2q^{7}-q^{8}+\cdots$
6050.2.a.t	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$3$	$0$	$-5$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-3q^{6}-5q^{7}-q^{8}+\cdots$
6050.2.a.u	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$-1$	$3$	$0$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-3q^{6}+q^{7}-q^{8}+\cdots$
6050.2.a.v	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$-3$	$0$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}-3q^{6}-q^{7}+q^{8}+\cdots$
6050.2.a.w	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$-2$	$0$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}-q^{7}+q^{8}+\cdots$
6050.2.a.x	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$-2$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots$
6050.2.a.y	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$1$	$-2$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots$
6050.2.a.z	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$-2$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots$
6050.2.a.ba	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$1$	$-2$	$0$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+3q^{7}+q^{8}+\cdots$
6050.2.a.bb	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$-2$	$0$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+4q^{7}+q^{8}+\cdots$
6050.2.a.bc	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$0$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots$
6050.2.a.bd	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
6050.2.a.be	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-3q^{9}-q^{13}+\cdots$
6050.2.a.bf	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-3q^{9}-q^{13}+\cdots$
6050.2.a.bg	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots$
6050.2.a.bh	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$0$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots$
6050.2.a.bi	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots$
6050.2.a.bj	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$0$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots$
6050.2.a.bk	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots$
6050.2.a.bl	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$1$	$2$	$0$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}-2q^{7}+q^{8}+\cdots$
6050.2.a.bm	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$1$	$1$	$2$	$0$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}-q^{7}+q^{8}+\cdots$
6050.2.a.bn	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$2$	$0$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}+3q^{7}+q^{8}+\cdots$
6050.2.a.bo	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$3$	$0$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}+3q^{6}-q^{7}+q^{8}+\cdots$
6050.2.a.bp	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$3$	$0$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}+3q^{6}-q^{7}+q^{8}+\cdots$
6050.2.a.bq	$6050$	$2$	6050.a	1.a	$1$	$1$	$1$	$48.309$	$\Q$	None	✓	$1$	$0$	$1$	$3$	$0$	$5$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}+3q^{6}+5q^{7}+q^{8}+\cdots$
6050.2.a.br	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$2$	$-2$	$-3$	$0$	$-6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots$
6050.2.a.bs	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$-3$	$0$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots$
6050.2.a.bt	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$-2$	$-2$	$0$	$-6$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta )q^{3}+q^{4}+(1-\beta )q^{6}+\cdots$
6050.2.a.bu	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$-2$	$0$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2\beta q^{3}+q^{4}+2\beta q^{6}+(-1+\cdots)q^{7}+\cdots$
6050.2.a.bv	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$-2$	$0$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2\beta q^{3}+q^{4}+2\beta q^{6}-\beta q^{7}+\cdots$
6050.2.a.bw	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$-2$	$-2$	$0$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta )q^{3}+q^{4}+(1-\beta )q^{6}+\cdots$
6050.2.a.bx	$6050$	$2$	6050.a	1.a	$1$	$2$	$2$	$48.309$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$-1$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+(-1+2\beta )q^{7}+\cdots$

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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.