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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
1089.6.a.b	$1089$	$6$	1089.a	1.a	$1$	$1$	$1$	$174.658$	$\Q$	None	✓	$1$	$1$	$-6$	$0$	$-6$	$40$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-6q^{2}+4q^{4}-6q^{5}+40q^{7}+168q^{8}+\cdots$
1089.6.a.c	$1089$	$6$	1089.a	1.a	$1$	$1$	$1$	$174.658$	$\Q$	None	✓	$1$	$1$	$-4$	$0$	$19$	$-10$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}-2^{4}q^{4}+19q^{5}-10q^{7}+192q^{8}+\cdots$
1089.6.a.d	$1089$	$6$	1089.a	1.a	$1$	$1$	$1$	$174.658$	$\Q$	None	✓	$1$	$1$	$-2$	$0$	$-46$	$-148$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-28q^{4}-46q^{5}-148q^{7}+\cdots$
1089.6.a.h	$1089$	$6$	1089.a	1.a	$1$	$1$	$1$	$174.658$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$92$	$26$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-31q^{4}+92q^{5}+26q^{7}-63q^{8}+\cdots$
1089.6.a.j	$1089$	$6$	1089.a	1.a	$1$	$2$	$2$	$174.658$	$\Q(\sqrt{177}) $	None	✓	$1$	$1$	$-5$	$0$	$-58$	$286$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2-\beta )q^{2}+(2^{4}+5\beta )q^{4}+(-24+\cdots)q^{5}+\cdots$
1089.6.a.k	$1089$	$6$	1089.a	1.a	$1$	$2$	$2$	$174.658$	$\Q(\sqrt{3}) $	$\Q(\sqrt{-3}) $	✓	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2^{5}q^{4}-149\beta q^{7}+116\beta q^{13}+2^{10}q^{16}+\cdots$
1089.6.a.o	$1089$	$6$	1089.a	1.a	$1$	$2$	$2$	$174.658$	$\Q(\sqrt{313}) $	None	✓	$1$	$1$	$1$	$0$	$38$	$18$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(46+\beta )q^{4}+(24-10\beta )q^{5}+\cdots$
1089.6.a.p	$1089$	$6$	1089.a	1.a	$1$	$2$	$2$	$174.658$	$\Q(\sqrt{33}) $	None	✓	$1$	$1$	$13$	$0$	$-58$	$-146$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(7-\beta )q^{2}+(5^{2}-13\beta )q^{4}+(-24+\cdots)q^{5}+\cdots$
1089.6.a.q	$1089$	$6$	1089.a	1.a	$1$	$3$	$3$	$174.658$	3.3.193425.1	None	✓	$1$	$1$	$-1$	$0$	$58$	$117$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(6+\beta _{1}+2\beta _{2})q^{4}+(17+6\beta _{1}+\cdots)q^{5}+\cdots$
1089.6.a.r	$1089$	$6$	1089.a	1.a	$1$	$3$	$3$	$174.658$	3.3.54492.1	None	✓	$1$	$1$	$0$	$0$	$-24$	$-84$	$-$	$-$	$+$	$3$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(28-2\beta _{1}-4\beta _{2})q^{4}+(-8+\cdots)q^{5}+\cdots$
1089.6.a.s	$1089$	$6$	1089.a	1.a	$1$	$3$	$3$	$174.658$	3.3.193425.1	None	✓	$1$	$1$	$1$	$0$	$58$	$-117$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(6+\beta _{1}+2\beta _{2})q^{4}+(17+6\beta _{1}+\cdots)q^{5}+\cdots$
1089.6.a.t	$1089$	$6$	1089.a	1.a	$1$	$4$	$4$	$174.658$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$1$	$-9$	$0$	$-42$	$-14$	$-$	$-$	$+$	$3$	$\mathrm{SU}(2)$	$q+(-2-\beta _{1})q^{2}+(12+6\beta _{1}+\beta _{2})q^{4}+\cdots$
1089.6.a.u	$1089$	$6$	1089.a	1.a	$1$	$4$	$4$	$174.658$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$1$	$9$	$0$	$-42$	$14$	$-$	$-$	$+$	$3$	$\mathrm{SU}(2)$	$q+(2+\beta _{1})q^{2}+(12+6\beta _{1}+\beta _{2})q^{4}+\cdots$
1089.6.a.v	$1089$	$6$	1089.a	1.a	$1$	$5$	$5$	$174.658$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	$1$	$1$	$-4$	$0$	$-29$	$-102$	$-$	$-$	$+$	$2^{5}\cdot 3$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(21-\beta _{1}+\beta _{3})q^{4}+\cdots$
1089.6.a.y	$1089$	$6$	1089.a	1.a	$1$	$5$	$5$	$174.658$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	$1$	$1$	$4$	$0$	$-29$	$102$	$-$	$-$	$+$	$2^{5}\cdot 3$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(21-\beta _{1}+\beta _{3})q^{4}+(-6+\cdots)q^{5}+\cdots$
1089.6.a.bb	$1089$	$6$	1089.a	1.a	$1$	$8$	$8$	$174.658$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-8$	$0$	$-70$	$292$	$-$	$-$	$+$	$2^{2}\cdot 11^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(11-\beta _{1}+\beta _{2})q^{4}+\cdots$
1089.6.a.bc	$1089$	$6$	1089.a	1.a	$1$	$8$	$8$	$174.658$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$2^{11}\cdot 3^{3}$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{2}+(19-\beta _{1})q^{4}-\beta _{2}q^{5}+\beta _{7}q^{7}+\cdots$
1089.6.a.bi	$1089$	$6$	1089.a	1.a	$1$	$10$	$10$	$174.658$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-7$	$0$	$33$	$-78$	$-$	$-$	$+$	$2^{2}\cdot 11^{4}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(15-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
1089.6.a.bl	$1089$	$6$	1089.a	1.a	$1$	$10$	$10$	$174.658$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$9$	$0$	$-11$	$-470$	$-$	$-$	$+$	$2^{2}\cdot 11^{4}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(19-\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
1089.6.a.bm	$1089$	$6$	1089.a	1.a	$1$	$12$	$12$	$174.658$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$2^{5}\cdot 3$	$\mathrm{SU}(2)$	$q+\beta _{6}q^{2}+(14+\beta _{3})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
1089.6.a.bn	$1089$	$6$	1089.a	1.a	$1$	$20$	$20$	$174.658$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$2$	$1$	$0$	$0$	$0$	$-472$	$+$	$+$	$+$	$2^{8}\cdot 3^{8}\cdot 5^{2}\cdot 11^{9}\cdot 31^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(15+\beta _{2})q^{4}+(-\beta _{1}-\beta _{8}+\cdots)q^{5}+\cdots$

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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.