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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 64 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	7	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4928.2.a.a	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$1$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}+q^{7}+6q^{9}-q^{11}+4q^{13}+\cdots$
4928.2.a.b	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$2$	$0$	$-2$	$-4$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-4q^{5}+q^{7}+q^{9}+q^{11}-4q^{13}+\cdots$
4928.2.a.c	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$2$	$0$	$-2$	$-2$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{5}-q^{7}+q^{9}-q^{11}-4q^{13}+\cdots$
4928.2.a.d	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$-2$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{5}-q^{7}+q^{9}-q^{11}+4q^{13}+\cdots$
4928.2.a.e	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$-2$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{5}+q^{7}+q^{9}+q^{11}+4q^{15}+\cdots$
4928.2.a.f	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$0$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{7}+q^{9}+q^{11}-6q^{17}+\cdots$
4928.2.a.g	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$2$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}-q^{7}+q^{9}-q^{11}-4q^{13}+\cdots$
4928.2.a.h	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$2$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}+q^{7}+q^{9}+q^{11}-4q^{13}+\cdots$
4928.2.a.i	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-3$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}+q^{7}-2q^{9}+q^{11}+4q^{13}+\cdots$
4928.2.a.j	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-1$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}-2q^{9}-q^{11}+2q^{13}+\cdots$
4928.2.a.k	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$1$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-q^{7}-2q^{9}+q^{11}-q^{15}+\cdots$
4928.2.a.l	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$1$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}-2q^{9}+q^{11}+4q^{13}+\cdots$
4928.2.a.m	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$3$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}+q^{7}-2q^{9}-q^{11}-6q^{13}+\cdots$
4928.2.a.n	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-2$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}-3q^{9}+q^{11}-2q^{13}+\cdots$
4928.2.a.o	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-2$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}-3q^{9}-q^{11}-2q^{13}+\cdots$
4928.2.a.p	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-3q^{9}-q^{11}+2q^{13}+4q^{17}+\cdots$
4928.2.a.q	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$0$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-3q^{9}+q^{11}+6q^{13}+2q^{19}+\cdots$
4928.2.a.r	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-3q^{9}-q^{11}+6q^{13}-2q^{19}+\cdots$
4928.2.a.s	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-3q^{9}+q^{11}+2q^{13}+4q^{17}+\cdots$
4928.2.a.t	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$2$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}-3q^{9}-q^{11}-2q^{13}+\cdots$
4928.2.a.u	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$2$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}-3q^{9}+q^{11}-2q^{13}+\cdots$
4928.2.a.v	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$4$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-q^{7}-3q^{9}+q^{11}-2q^{13}+\cdots$
4928.2.a.w	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$4$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+q^{7}-3q^{9}-q^{11}-2q^{13}+\cdots$
4928.2.a.x	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-3$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}-q^{7}-2q^{9}-q^{11}+4q^{13}+\cdots$
4928.2.a.y	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-1$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}-2q^{9}+q^{11}+2q^{13}+\cdots$
4928.2.a.z	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$1$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}-2q^{9}-q^{11}+4q^{13}+\cdots$
4928.2.a.ba	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$1$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{7}-2q^{9}-q^{11}+q^{15}+\cdots$
4928.2.a.bb	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$3$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}-q^{7}-2q^{9}+q^{11}-6q^{13}+\cdots$
4928.2.a.bc	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$-4$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-4q^{5}-q^{7}+q^{9}-q^{11}-4q^{13}+\cdots$
4928.2.a.bd	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$-2$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}-q^{7}+q^{9}-q^{11}-4q^{15}+\cdots$
4928.2.a.be	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$-2$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}+q^{7}+q^{9}+q^{11}-4q^{13}+\cdots$
4928.2.a.bf	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$-2$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}+q^{7}+q^{9}+q^{11}+4q^{13}+\cdots$
4928.2.a.bg	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$0$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{7}+q^{9}-q^{11}-6q^{17}+\cdots$
4928.2.a.bh	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$2$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{5}-q^{7}+q^{9}-q^{11}-4q^{13}+\cdots$
4928.2.a.bi	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$2$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{5}+q^{7}+q^{9}+q^{11}-4q^{13}+\cdots$
4928.2.a.bj	$4928$	$2$	4928.a	1.a	$1$	$1$	$1$	$39.350$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$1$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{5}-q^{7}+6q^{9}+q^{11}+4q^{13}+\cdots$
4928.2.a.bk	$4928$	$2$	4928.a	1.a	$1$	$2$	$2$	$39.350$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-2$	$-2$	$-2$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(-1-\beta )q^{5}-q^{7}+\cdots$
4928.2.a.bl	$4928$	$2$	4928.a	1.a	$1$	$2$	$2$	$39.350$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-2\beta q^{5}+q^{7}+(1-2\beta )q^{9}+\cdots$
4928.2.a.bm	$4928$	$2$	4928.a	1.a	$1$	$2$	$2$	$39.350$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-2$	$4$	$2$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+2q^{5}+q^{7}+(3+2\beta )q^{9}+\cdots$
4928.2.a.bn	$4928$	$2$	4928.a	1.a	$1$	$2$	$2$	$39.350$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$-1$	$-1$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-\beta q^{5}-q^{7}+(1+\beta )q^{9}-q^{11}+\cdots$
4928.2.a.bo	$4928$	$2$	4928.a	1.a	$1$	$2$	$2$	$39.350$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$-1$	$3$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(2-\beta )q^{5}+q^{7}+(1+\beta )q^{9}+\cdots$
4928.2.a.bp	$4928$	$2$	4928.a	1.a	$1$	$2$	$2$	$39.350$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$0$	$0$	$-4$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2q^{5}-q^{7}+3q^{9}+q^{11}+\cdots$
4928.2.a.bq	$4928$	$2$	4928.a	1.a	$1$	$2$	$2$	$39.350$	$\Q(\sqrt{6}) $	None	✓	$1$	$1$	$0$	$0$	$-4$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2q^{5}+q^{7}+3q^{9}-q^{11}+\cdots$
4928.2.a.br	$4928$	$2$	4928.a	1.a	$1$	$2$	$2$	$39.350$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$1$	$-1$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{5}+q^{7}+(1+\beta )q^{9}+q^{11}+\cdots$
4928.2.a.bs	$4928$	$2$	4928.a	1.a	$1$	$2$	$2$	$39.350$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$1$	$3$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(2-\beta )q^{5}-q^{7}+(1+\beta )q^{9}+\cdots$
4928.2.a.bt	$4928$	$2$	4928.a	1.a	$1$	$2$	$2$	$39.350$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$2$	$-2$	$2$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-1-\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots$
4928.2.a.bu	$4928$	$2$	4928.a	1.a	$1$	$2$	$2$	$39.350$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+2\beta q^{5}-q^{7}+(1+2\beta )q^{9}+\cdots$
4928.2.a.bv	$4928$	$2$	4928.a	1.a	$1$	$2$	$2$	$39.350$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$2$	$4$	$-2$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+2q^{5}-q^{7}+(3+2\beta )q^{9}+\cdots$
4928.2.a.bw	$4928$	$2$	4928.a	1.a	$1$	$3$	$3$	$39.350$	3.3.229.1	None	✓	$1$	$0$	$0$	$-1$	$-1$	$3$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+\beta _{2}q^{5}+q^{7}+(1-\beta _{1})q^{9}+\cdots$
4928.2.a.bx	$4928$	$2$	4928.a	1.a	$1$	$3$	$3$	$39.350$	3.3.1016.1	None	✓	$1$	$1$	$0$	$-1$	$1$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}-q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$

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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.