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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 (21 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1089.4.a.a	$1089$	$4$	1089.a	1.a	$1$	$1$	$1$	$64.253$	$\Q$	None	✓	$1$	$0$	$-5$	$0$	$14$	$32$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-5q^{2}+17q^{4}+14q^{5}+2^{5}q^{7}-45q^{8}+\cdots$
1089.4.a.b	$1089$	$4$	1089.a	1.a	$1$	$1$	$1$	$64.253$	$\Q$	None	✓	$1$	$0$	$-4$	$0$	$13$	$26$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}+8q^{4}+13q^{5}+26q^{7}-52q^{10}+\cdots$
1089.4.a.d	$1089$	$4$	1089.a	1.a	$1$	$1$	$1$	$64.253$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$-7$	$4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-7q^{4}-7q^{5}+4q^{7}+15q^{8}+\cdots$
1089.4.a.e	$1089$	$4$	1089.a	1.a	$1$	$1$	$1$	$64.253$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$4$	$26$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-7q^{4}+4q^{5}+26q^{7}+15q^{8}+\cdots$
1089.4.a.h	$1089$	$4$	1089.a	1.a	$1$	$1$	$1$	$64.253$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-7$	$-4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-7q^{4}-7q^{5}-4q^{7}-15q^{8}+\cdots$
1089.4.a.j	$1089$	$4$	1089.a	1.a	$1$	$1$	$1$	$64.253$	$\Q$	None	✓	$1$	$0$	$4$	$0$	$13$	$-26$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{2}+8q^{4}+13q^{5}-26q^{7}+52q^{10}+\cdots$
1089.4.a.k	$1089$	$4$	1089.a	1.a	$1$	$2$	$2$	$64.253$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$-2$	$0$	$10$	$8$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(5-2\beta )q^{4}+(5-\beta )q^{5}+\cdots$
1089.4.a.m	$1089$	$4$	1089.a	1.a	$1$	$2$	$2$	$64.253$	$\Q(\sqrt{3}) $	$\Q(\sqrt{-3}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$2\cdot 3^{2}$	$N(\mathrm{U}(1))$	$q-8q^{4}-\beta q^{7}-2\beta q^{13}+2^{6}q^{16}+\cdots$
1089.4.a.q	$1089$	$4$	1089.a	1.a	$1$	$2$	$2$	$64.253$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$0$	$13$	$44$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(2-4\beta )q^{2}+12q^{4}+(12-11\beta )q^{5}+\cdots$
1089.4.a.t	$1089$	$4$	1089.a	1.a	$1$	$2$	$2$	$64.253$	$\Q(\sqrt{33}) $	None	✓	$1$	$0$	$1$	$0$	$-16$	$-2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+\beta q^{4}+(-10+4\beta )q^{5}+(-2+\cdots)q^{7}+\cdots$
1089.4.a.u	$1089$	$4$	1089.a	1.a	$1$	$2$	$2$	$64.253$	$\Q(\sqrt{97}) $	None	✓	$1$	$0$	$1$	$0$	$14$	$-24$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(2^{4}+\beta )q^{4}+(6+2\beta )q^{5}+(-14+\cdots)q^{7}+\cdots$
1089.4.a.v	$1089$	$4$	1089.a	1.a	$1$	$2$	$2$	$64.253$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$0$	$-2$	$-20$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(-4+2\beta )q^{4}+(-1-8\beta )q^{5}+\cdots$
1089.4.a.x	$1089$	$4$	1089.a	1.a	$1$	$2$	$2$	$64.253$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$0$	$10$	$-8$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(5+2\beta )q^{4}+(5+\beta )q^{5}+\cdots$
1089.4.a.z	$1089$	$4$	1089.a	1.a	$1$	$4$	$4$	$64.253$	4.4.5225.1	None	✓	$1$	$0$	$-3$	$0$	$-12$	$11$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1}-\beta _{2})q^{2}+(-2+3\beta _{1}+\cdots)q^{4}+\cdots$
1089.4.a.ba	$1089$	$4$	1089.a	1.a	$1$	$4$	$4$	$64.253$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$0$	$-1$	$0$	$-14$	$-20$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(6+\beta _{1}+\beta _{3})q^{4}+(-3+\beta _{2}+\cdots)q^{5}+\cdots$
1089.4.a.be	$1089$	$4$	1089.a	1.a	$1$	$4$	$4$	$64.253$	$\Q(\sqrt{5}, \sqrt{17})$	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$2^{6}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+9q^{4}-\beta _{3}q^{5}+\beta _{2}q^{7}+\beta _{1}q^{8}+\cdots$
1089.4.a.bf	$1089$	$4$	1089.a	1.a	$1$	$4$	$4$	$64.253$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$0$	$1$	$0$	$-14$	$20$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(6+\beta _{1}+\beta _{3})q^{4}+(-3+\beta _{2}+\cdots)q^{5}+\cdots$
1089.4.a.bh	$1089$	$4$	1089.a	1.a	$1$	$4$	$4$	$64.253$	$\Q(\sqrt{5}, \sqrt{37})$	None	✓	$1$	$0$	$4$	$0$	$11$	$-25$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1}+\beta _{2})q^{2}+(3+\beta _{1}+\beta _{2}+2\beta _{3})q^{4}+\cdots$
1089.4.a.bk	$1089$	$4$	1089.a	1.a	$1$	$6$	$6$	$64.253$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$0$	$5$	$0$	$-9$	$-1$	$-$	$-$	$+$	$11$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(3-\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots$
1089.4.a.bm	$1089$	$4$	1089.a	1.a	$1$	$12$	$12$	$64.253$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$0$	$66$	$+$	$+$	$+$	$2^{2}\cdot 11^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(5+\beta _{2})q^{4}+(\beta _{1}+\beta _{5})q^{5}+\cdots$
1089.4.a.bn	$1089$	$4$	1089.a	1.a	$1$	$12$	$12$	$64.253$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$2^{5}\cdot 3$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(6+\beta _{7})q^{4}+\beta _{4}q^{5}+(-2\beta _{2}+\cdots)q^{7}+\cdots$

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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.