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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 85 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
8624.2.a.a	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$0$	$0$	$-3$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}+6q^{9}+q^{11}+4q^{13}+\cdots$
8624.2.a.b	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+2q^{5}+6q^{9}+q^{11}-7q^{13}+\cdots$
8624.2.a.c	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$3$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+3q^{5}+6q^{9}+q^{11}-9q^{15}+\cdots$
8624.2.a.d	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$0$	$0$	$-3$	$4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+4q^{5}+6q^{9}+q^{11}+q^{13}+\cdots$
8624.2.a.e	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$-2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{5}+q^{9}+q^{11}-4q^{13}+\cdots$
8624.2.a.f	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}+q^{11}-2q^{13}+2q^{17}+\cdots$
8624.2.a.g	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}+q^{9}-q^{11}-2q^{13}+\cdots$
8624.2.a.h	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+4q^{5}+q^{9}-q^{11}+2q^{13}+\cdots$
8624.2.a.i	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-2q^{9}+q^{11}-3q^{13}+\cdots$
8624.2.a.j	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{9}-q^{11}-4q^{13}+\cdots$
8624.2.a.k	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{9}+q^{11}-q^{13}-6q^{17}+\cdots$
8624.2.a.l	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{9}+q^{11}+5q^{13}+6q^{17}+\cdots$
8624.2.a.m	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$1$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{9}-q^{11}-q^{15}+2q^{17}+\cdots$
8624.2.a.n	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{9}-q^{11}+4q^{13}+\cdots$
8624.2.a.o	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-3q^{9}+q^{11}-2q^{13}-2q^{17}+\cdots$
8624.2.a.p	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{9}+q^{11}+6q^{13}-2q^{19}-4q^{23}+\cdots$
8624.2.a.q	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-3q^{9}+q^{11}-2q^{13}+2q^{17}+\cdots$
8624.2.a.r	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-3q^{9}+q^{11}-2q^{13}+4q^{17}+\cdots$
8624.2.a.s	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-3$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}-2q^{9}+q^{11}+4q^{13}+\cdots$
8624.2.a.t	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{9}+q^{11}-5q^{13}-6q^{17}+\cdots$
8624.2.a.u	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{9}+q^{11}+q^{13}+6q^{17}+\cdots$
8624.2.a.v	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$2$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-2q^{9}+q^{11}+3q^{13}+\cdots$
8624.2.a.w	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$3$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}-2q^{9}+q^{11}+4q^{13}+\cdots$
8624.2.a.x	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$-4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-4q^{5}+q^{9}-q^{11}-2q^{13}+\cdots$
8624.2.a.y	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$-2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}+q^{9}-q^{11}+2q^{13}+\cdots$
8624.2.a.z	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$-2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}+q^{9}-q^{11}+4q^{13}+\cdots$
8624.2.a.ba	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$-2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}+q^{9}+q^{11}-4q^{15}+\cdots$
8624.2.a.bb	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}+q^{11}+2q^{13}-2q^{17}+\cdots$
8624.2.a.bc	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{5}+q^{9}-q^{11}-4q^{13}+\cdots$
8624.2.a.bd	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$1$	$0$	$3$	$-4$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-4q^{5}+6q^{9}+q^{11}-q^{13}+\cdots$
8624.2.a.be	$8624$	$2$	8624.a	1.a	$1$	$1$	$1$	$68.863$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$-2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-2q^{5}+6q^{9}+q^{11}+7q^{13}+\cdots$
8624.2.a.bf	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-2$	$-2$	$0$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(-1-\beta )q^{5}+(3+2\beta )q^{9}+\cdots$
8624.2.a.bg	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+\beta q^{5}-2\beta q^{9}-q^{11}+\cdots$
8624.2.a.bh	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$-2$	$4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(2+\beta )q^{5}-2\beta q^{9}+\cdots$
8624.2.a.bi	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$-1$	$3$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(2-\beta )q^{5}+(1+\beta )q^{9}-q^{11}+\cdots$
8624.2.a.bj	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$0$	$0$	$-4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2q^{5}+3q^{9}+q^{11}+(-2+\cdots)q^{13}+\cdots$
8624.2.a.bk	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{7}) $	None	✓	$1$	$1$	$0$	$0$	$-2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1+\beta )q^{5}+4q^{9}-q^{11}+\cdots$
8624.2.a.bl	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{5}-3q^{9}-q^{11}+3\beta q^{13}-2\beta q^{17}+\cdots$
8624.2.a.bm	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-3q^{9}-q^{11}-3\beta q^{13}-\beta q^{17}+\cdots$
8624.2.a.bn	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2\beta q^{5}-3q^{9}-q^{11}-\beta q^{13}+2\beta q^{17}+\cdots$
8624.2.a.bo	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}-3q^{9}-q^{11}-2\beta q^{13}-\beta q^{17}+\cdots$
8624.2.a.bp	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}-3q^{9}+q^{11}+\beta q^{17}-\beta q^{19}+\cdots$
8624.2.a.bq	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{5}-q^{9}-q^{11}-2q^{15}+\cdots$
8624.2.a.br	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+\beta q^{5}-q^{9}-q^{11}-2\beta q^{13}+\cdots$
8624.2.a.bs	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-3\beta q^{5}-q^{9}+q^{11}-6q^{15}+\cdots$
8624.2.a.bt	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{5}-q^{9}+q^{11}-2q^{15}+\cdots$
8624.2.a.bu	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{9}+q^{11}+\beta q^{13}+5\beta q^{17}+\cdots$
8624.2.a.bv	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+\beta q^{5}-q^{9}+q^{11}+2q^{15}+\cdots$
8624.2.a.bw	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+\beta q^{5}-q^{9}+q^{11}+2\beta q^{13}+\cdots$
8624.2.a.bx	$8624$	$2$	8624.a	1.a	$1$	$2$	$2$	$68.863$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{3}-\beta q^{5}+5q^{9}+q^{11}+\beta q^{13}+\cdots$

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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.