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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 81 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	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9800.2.a.a	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+6q^{9}-5q^{11}-5q^{13}-7q^{17}+\cdots$
9800.2.a.b	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+6q^{9}-q^{11}-2q^{13}-3q^{17}+\cdots$
9800.2.a.c	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+6q^{9}+q^{11}+4q^{13}+5q^{17}+\cdots$
9800.2.a.d	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}-4q^{11}-4q^{13}+4q^{19}+\cdots$
9800.2.a.e	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}-3q^{11}+2q^{13}-4q^{17}+\cdots$
9800.2.a.f	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}-3q^{11}+2q^{13}-4q^{17}+\cdots$
9800.2.a.g	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}-q^{11}-3q^{13}-2q^{17}+\cdots$
9800.2.a.h	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}+q^{11}-4q^{13}-6q^{19}+\cdots$
9800.2.a.i	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}+4q^{11}-2q^{13}+2q^{19}+\cdots$
9800.2.a.j	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}+4q^{11}+2q^{13}+3q^{17}+\cdots$
9800.2.a.k	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}+4q^{11}+2q^{13}+3q^{17}+\cdots$
9800.2.a.l	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}+5q^{11}-8q^{17}+2q^{19}+\cdots$
9800.2.a.m	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$2$	$0$	$-1$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{9}-5q^{11}-7q^{13}+3q^{17}+\cdots$
9800.2.a.n	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{9}-5q^{11}+q^{13}+3q^{17}+\cdots$
9800.2.a.o	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{9}-2q^{11}+4q^{13}-6q^{19}+\cdots$
9800.2.a.p	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{9}-q^{11}+q^{13}+3q^{17}+\cdots$
9800.2.a.q	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{9}-q^{11}+6q^{13}-7q^{17}+\cdots$
9800.2.a.r	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{9}+2q^{11}-4q^{17}-2q^{19}+\cdots$
9800.2.a.s	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{9}+3q^{11}-6q^{13}-5q^{17}+\cdots$
9800.2.a.t	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{9}+3q^{11}+q^{13}-5q^{17}+\cdots$
9800.2.a.u	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{9}-4q^{11}+2q^{13}-6q^{17}-8q^{19}+\cdots$
9800.2.a.v	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{9}+q^{11}-2q^{13}-4q^{17}+2q^{19}+\cdots$
9800.2.a.w	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{9}+q^{11}+2q^{13}+4q^{17}+2q^{19}+\cdots$
9800.2.a.x	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{9}+4q^{11}-2q^{13}+2q^{17}-4q^{19}+\cdots$
9800.2.a.y	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{9}-5q^{11}+7q^{13}-3q^{17}+\cdots$
9800.2.a.z	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{9}-2q^{11}-4q^{13}+6q^{19}+\cdots$
9800.2.a.ba	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{9}-q^{11}-6q^{13}+7q^{17}+\cdots$
9800.2.a.bb	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{9}-q^{11}-q^{13}-3q^{17}+\cdots$
9800.2.a.bc	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{9}+2q^{11}+4q^{17}+2q^{19}+\cdots$
9800.2.a.bd	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{9}+3q^{11}-q^{13}+5q^{17}+\cdots$
9800.2.a.be	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{9}+3q^{11}+6q^{13}+5q^{17}+\cdots$
9800.2.a.bf	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}-4q^{11}+4q^{13}+4q^{19}+\cdots$
9800.2.a.bg	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}-3q^{11}-2q^{13}+4q^{17}+\cdots$
9800.2.a.bh	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}-3q^{11}-2q^{13}+4q^{17}+\cdots$
9800.2.a.bi	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}-q^{11}+3q^{13}+2q^{17}+\cdots$
9800.2.a.bj	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}-2q^{17}+2q^{19}-8q^{23}+\cdots$
9800.2.a.bk	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}+q^{11}+4q^{13}-6q^{19}+\cdots$
9800.2.a.bl	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}+4q^{11}-2q^{13}-3q^{17}+\cdots$
9800.2.a.bm	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}+4q^{11}-2q^{13}-3q^{17}+\cdots$
9800.2.a.bn	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}+4q^{11}+2q^{13}-2q^{19}+\cdots$
9800.2.a.bo	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}+5q^{11}+8q^{17}+2q^{19}+\cdots$
9800.2.a.bp	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+6q^{9}-q^{11}+2q^{13}+3q^{17}+\cdots$
9800.2.a.bq	$9800$	$2$	9800.a	1.a	$1$	$1$	$1$	$78.253$	$\Q$	None	✓	$1$	$1$	$0$	$3$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+6q^{9}+q^{11}-4q^{13}-5q^{17}+\cdots$
9800.2.a.br	$9800$	$2$	9800.a	1.a	$1$	$2$	$2$	$78.253$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-2\beta q^{9}+(-2+2\beta )q^{11}+\cdots$
9800.2.a.bs	$9800$	$2$	9800.a	1.a	$1$	$2$	$2$	$78.253$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-2\beta q^{9}-q^{11}+(-1+\cdots)q^{13}+\cdots$
9800.2.a.bt	$9800$	$2$	9800.a	1.a	$1$	$2$	$2$	$78.253$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$-1$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1+\beta )q^{9}+(-3+2\beta )q^{11}+\cdots$
9800.2.a.bu	$9800$	$2$	9800.a	1.a	$1$	$2$	$2$	$78.253$	$\Q(\sqrt{33}) $	None	✓	$1$	$0$	$0$	$-1$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(5+\beta )q^{9}+(4-\beta )q^{11}+(2+\cdots)q^{13}+\cdots$
9800.2.a.bv	$9800$	$2$	9800.a	1.a	$1$	$2$	$2$	$78.253$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{9}+6q^{11}-4\beta q^{13}+\beta q^{17}+\cdots$
9800.2.a.bw	$9800$	$2$	9800.a	1.a	$1$	$2$	$2$	$78.253$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{3}+5q^{9}-4q^{11}-\beta q^{13}-2\beta q^{17}+\cdots$
9800.2.a.bx	$9800$	$2$	9800.a	1.a	$1$	$2$	$2$	$78.253$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$1$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1+\beta )q^{9}+(-3+2\beta )q^{11}+\cdots$

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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.