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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 (23 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	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1200.4.a.c	$1200$	$4$	1200.a	1.a	$1$	$1$	$1$	$70.802$	$\Q$	None	✓	$1$	$0$	$0$	$-3$	$0$	$-16$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-2^{4}q^{7}+9q^{9}+28q^{11}+26q^{13}+\cdots$
1200.4.a.h	$1200$	$4$	1200.a	1.a	$1$	$1$	$1$	$70.802$	$\Q$	None	✓	$1$	$0$	$0$	$-3$	$0$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-2q^{7}+9q^{9}-70q^{11}-54q^{13}+\cdots$
1200.4.a.j	$1200$	$4$	1200.a	1.a	$1$	$1$	$1$	$70.802$	$\Q$	None	✓	$1$	$0$	$0$	$-3$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+9q^{9}-4q^{11}-54q^{13}-114q^{17}+\cdots$
1200.4.a.k	$1200$	$4$	1200.a	1.a	$1$	$1$	$1$	$70.802$	$\Q$	None	✓	$1$	$0$	$0$	$-3$	$0$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+4q^{7}+9q^{9}-72q^{11}+6q^{13}+\cdots$
1200.4.a.m	$1200$	$4$	1200.a	1.a	$1$	$1$	$1$	$70.802$	$\Q$	None	✓	$1$	$0$	$0$	$-3$	$0$	$7$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+7q^{7}+9q^{9}+54q^{11}-55q^{13}+\cdots$
1200.4.a.p	$1200$	$4$	1200.a	1.a	$1$	$1$	$1$	$70.802$	$\Q$	None	✓	$1$	$0$	$0$	$-3$	$0$	$20$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+20q^{7}+9q^{9}+56q^{11}+86q^{13}+\cdots$
1200.4.a.q	$1200$	$4$	1200.a	1.a	$1$	$1$	$1$	$70.802$	$\Q$	None	✓	$1$	$0$	$0$	$-3$	$0$	$22$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+22q^{7}+9q^{9}+14q^{11}+30q^{13}+\cdots$
1200.4.a.t	$1200$	$4$	1200.a	1.a	$1$	$1$	$1$	$70.802$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$0$	$-24$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-24q^{7}+9q^{9}-52q^{11}-22q^{13}+\cdots$
1200.4.a.y	$1200$	$4$	1200.a	1.a	$1$	$1$	$1$	$70.802$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$0$	$-7$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-7q^{7}+9q^{9}+54q^{11}+55q^{13}+\cdots$
1200.4.a.z	$1200$	$4$	1200.a	1.a	$1$	$1$	$1$	$70.802$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$0$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-4q^{7}+9q^{9}+28q^{11}-2^{4}q^{13}+\cdots$
1200.4.a.ba	$1200$	$4$	1200.a	1.a	$1$	$1$	$1$	$70.802$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$0$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-4q^{7}+9q^{9}+48q^{11}-2q^{13}+\cdots$
1200.4.a.be	$1200$	$4$	1200.a	1.a	$1$	$1$	$1$	$70.802$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$0$	$8$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+8q^{7}+9q^{9}-6^{2}q^{11}+10q^{13}+\cdots$
1200.4.a.bg	$1200$	$4$	1200.a	1.a	$1$	$1$	$1$	$70.802$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$0$	$10$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+10q^{7}+9q^{9}+14q^{11}+82q^{13}+\cdots$
1200.4.a.bh	$1200$	$4$	1200.a	1.a	$1$	$1$	$1$	$70.802$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$0$	$10$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+10q^{7}+9q^{9}+46q^{11}+34q^{13}+\cdots$
1200.4.a.bk	$1200$	$4$	1200.a	1.a	$1$	$1$	$1$	$70.802$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$0$	$32$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+2^{5}q^{7}+9q^{9}+60q^{11}+34q^{13}+\cdots$
1200.4.a.bl	$1200$	$4$	1200.a	1.a	$1$	$2$	$2$	$70.802$	$\Q(\sqrt{19}) $	None	✓	$1$	$0$	$0$	$-6$	$0$	$-26$	$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-3q^{3}+(-13+\beta )q^{7}+9q^{9}+(-14+\cdots)q^{11}+\cdots$
1200.4.a.bm	$1200$	$4$	1200.a	1.a	$1$	$2$	$2$	$70.802$	$\Q(\sqrt{181}) $	None	✓	$1$	$0$	$0$	$-6$	$0$	$-6$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-3q^{3}+(-3-\beta )q^{7}+9q^{9}+(-4+\cdots)q^{11}+\cdots$
1200.4.a.bn	$1200$	$4$	1200.a	1.a	$1$	$2$	$2$	$70.802$	$\Q(\sqrt{41}) $	None	✓	$1$	$0$	$0$	$-6$	$0$	$-6$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-3q^{3}+(-3-3\beta )q^{7}+9q^{9}+(21+\cdots)q^{11}+\cdots$
1200.4.a.bp	$1200$	$4$	1200.a	1.a	$1$	$2$	$2$	$70.802$	$\Q(\sqrt{109}) $	None	✓	$1$	$0$	$0$	$-6$	$0$	$2$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-3q^{3}+(1+\beta )q^{7}+9q^{9}+(8-3\beta )q^{11}+\cdots$
1200.4.a.bq	$1200$	$4$	1200.a	1.a	$1$	$2$	$2$	$70.802$	$\Q(\sqrt{129}) $	None	✓	$1$	$0$	$0$	$6$	$0$	$-2$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+3q^{3}+(-1-3\beta )q^{7}+9q^{9}+(-37+\cdots)q^{11}+\cdots$
1200.4.a.br	$1200$	$4$	1200.a	1.a	$1$	$2$	$2$	$70.802$	$\Q(\sqrt{109}) $	None	✓	$1$	$0$	$0$	$6$	$0$	$-2$	$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+3q^{3}+(-1-\beta )q^{7}+9q^{9}+(8-3\beta )q^{11}+\cdots$
1200.4.a.bs	$1200$	$4$	1200.a	1.a	$1$	$2$	$2$	$70.802$	$\Q(\sqrt{181}) $	None	✓	$1$	$0$	$0$	$6$	$0$	$6$	$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+3q^{3}+(3+\beta )q^{7}+9q^{9}+(-4-\beta )q^{11}+\cdots$
1200.4.a.bu	$1200$	$4$	1200.a	1.a	$1$	$2$	$2$	$70.802$	$\Q(\sqrt{19}) $	None	✓	$1$	$0$	$0$	$6$	$0$	$26$	$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+3q^{3}+(13+\beta )q^{7}+9q^{9}+(-14+\cdots)q^{11}+\cdots$

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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.