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Note: Search results may be incomplete due to uncomputed quantities: fricke_eigenval (110727 objects)

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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 (24 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	5	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4200.2.a.d	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-5q^{11}-4q^{13}+\cdots$
4200.2.a.e	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots$
4200.2.a.g	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-2q^{11}-5q^{13}+\cdots$
4200.2.a.l	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+2q^{11}+3q^{13}+\cdots$
4200.2.a.n	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
4200.2.a.o	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+5q^{11}+2q^{13}+\cdots$
4200.2.a.p	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-5q^{11}+4q^{13}+\cdots$
4200.2.a.q	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$
4200.2.a.s	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-2q^{11}+5q^{13}+\cdots$
4200.2.a.v	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+2q^{11}-3q^{13}+\cdots$
4200.2.a.w	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
4200.2.a.x	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
4200.2.a.z	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
4200.2.a.ba	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+5q^{11}-2q^{13}+\cdots$
4200.2.a.be	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-2q^{13}-2q^{17}+\cdots$
4200.2.a.bf	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
4200.2.a.bg	$4200$	$2$	4200.a	1.a	$1$	$2$	$2$	$33.537$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$-2$	$-$	$+$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+\beta q^{11}-2q^{13}+\cdots$
4200.2.a.bh	$4200$	$2$	4200.a	1.a	$1$	$2$	$2$	$33.537$	$\Q(\sqrt{73}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$-2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+\beta q^{11}+(-1-\beta )q^{13}+\cdots$
4200.2.a.bi	$4200$	$2$	4200.a	1.a	$1$	$2$	$2$	$33.537$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$-2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+(1+\beta )q^{11}+(-2+\cdots)q^{13}+\cdots$
4200.2.a.bj	$4200$	$2$	4200.a	1.a	$1$	$2$	$2$	$33.537$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$2$	$-$	$+$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-2q^{11}-\beta q^{13}+\cdots$
4200.2.a.bl	$4200$	$2$	4200.a	1.a	$1$	$2$	$2$	$33.537$	$\Q(\sqrt{73}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+\beta q^{11}+(1+\beta )q^{13}+\cdots$
4200.2.a.bm	$4200$	$2$	4200.a	1.a	$1$	$2$	$2$	$33.537$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+(1+\beta )q^{11}+(2-3\beta )q^{13}+\cdots$
4200.2.a.bn	$4200$	$2$	4200.a	1.a	$1$	$3$	$3$	$33.537$	3.3.148.1	None	✓	$1$	$0$	$0$	$-3$	$0$	$-3$	$+$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+(-1-\beta _{1}+\beta _{2})q^{11}+\cdots$
4200.2.a.bq	$4200$	$2$	4200.a	1.a	$1$	$3$	$3$	$33.537$	3.3.148.1	None	✓	$1$	$0$	$0$	$3$	$0$	$3$	$+$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+(1+\beta _{1}+\beta _{2})q^{11}+\cdots$

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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.