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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 (27 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2916.1.d.a	$2916$	$1$	2916.d	4.b	$2$	$3$	$3$	$1.455$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-1}) $	None	✓	$2$	$0$	$-3$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}+\beta _{1}q^{5}-q^{8}-\beta _{1}q^{10}+\cdots$
2916.1.d.b	$2916$	$1$	2916.d	4.b	$2$	$3$	$3$	$1.455$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-1}) $	None	✓	$2$	$0$	$3$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}-\beta _{1}q^{5}+q^{8}-\beta _{1}q^{10}+\cdots$
2916.1.f.a	$2916$	$1$	2916.f	36.f	$6$	$6$	$3$	$1.455$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$		$3$		$q-\zeta_{18}^{3}q^{2}+\zeta_{18}^{6}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{8}+\cdots)q^{5}+\cdots$
2916.1.f.b	$2916$	$1$	2916.f	36.f	$6$	$6$	$3$	$1.455$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$3$	$0$	$0$	$0$		$3$		$q+\zeta_{18}^{3}q^{2}+\zeta_{18}^{6}q^{4}+(\zeta_{18}-\zeta_{18}^{2}+\cdots)q^{5}+\cdots$
2916.1.j.a	$2916$	$1$	2916.j	108.j	$18$	$6$	$1$	$1.455$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-6$	$0$		$1$		$q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+(-1-\zeta_{18}^{4}+\cdots)q^{5}+\cdots$
2916.1.j.b	$2916$	$1$	2916.j	108.j	$18$	$6$	$1$	$1.455$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-3$	$0$		$1$		$q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+(\zeta_{18}^{6}-\zeta_{18}^{7}+\cdots)q^{5}+\cdots$
2916.1.j.c	$2916$	$1$	2916.j	108.j	$18$	$6$	$1$	$1.455$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-3$	$0$		$1$		$q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+(-\zeta_{18}-\zeta_{18}^{3}+\cdots)q^{5}+\cdots$
2916.1.j.d	$2916$	$1$	2916.j	108.j	$18$	$6$	$1$	$1.455$	$\Q(\zeta_{18})$	$D_{3}$	$\Q(\sqrt{-1}) $	None		$12$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}-\zeta_{18}^{2}q^{5}+\cdots$
2916.1.j.e	$2916$	$1$	2916.j	108.j	$18$	$6$	$1$	$1.455$	$\Q(\zeta_{18})$	$D_{3}$	$\Q(\sqrt{-1}) $	None		$12$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+\zeta_{18}^{2}q^{5}+\cdots$
2916.1.j.f	$2916$	$1$	2916.j	108.j	$18$	$6$	$1$	$1.455$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$3$	$0$		$1$		$q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+(-\zeta_{18}^{6}+\zeta_{18}^{7}+\cdots)q^{5}+\cdots$
2916.1.j.g	$2916$	$1$	2916.j	108.j	$18$	$6$	$1$	$1.455$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$3$	$0$		$1$		$q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+(\zeta_{18}+\zeta_{18}^{3}+\cdots)q^{5}+\cdots$
2916.1.j.h	$2916$	$1$	2916.j	108.j	$18$	$6$	$1$	$1.455$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$6$	$0$		$1$		$q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+(1+\zeta_{18}^{4}+\cdots)q^{5}+\cdots$
2916.1.k.a	$2916$	$1$	2916.k	27.f	$18$	$6$	$1$	$1.455$	$\Q(\zeta_{18})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		$12$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{8}q^{7}+\zeta_{18}^{4}q^{13}+\zeta_{18}^{6}q^{19}+\cdots$
2916.1.k.b	$2916$	$1$	2916.k	27.f	$18$	$6$	$1$	$1.455$	$\Q(\zeta_{18})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		$12$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{8}q^{7}-\zeta_{18}^{4}q^{13}-\zeta_{18}^{6}q^{19}+\cdots$
2916.1.k.c	$2916$	$1$	2916.k	27.f	$18$	$6$	$1$	$1.455$	$\Q(\zeta_{18})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		$12$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{8}q^{7}-\zeta_{18}^{4}q^{13}-\zeta_{18}^{6}q^{19}+\cdots$
2916.2.a.a	$2916$	$2$	2916.a	1.a	$1$	$3$	$3$	$23.284$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}-\beta _{1}q^{7}+(2-\beta _{1}+\beta _{2})q^{11}+\cdots$
2916.2.a.b	$2916$	$2$	2916.a	1.a	$1$	$3$	$3$	$23.284$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{5}-\beta _{1}q^{7}+(-2+\beta _{1}-\beta _{2})q^{11}+\cdots$
2916.2.a.c	$2916$	$2$	2916.a	1.a	$1$	$9$	$9$	$23.284$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-6$	$0$	$+$	$3^{3}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{5}+\beta _{6}q^{7}+(-1-\beta _{3}+\cdots)q^{11}+\cdots$
2916.2.a.d	$2916$	$2$	2916.a	1.a	$1$	$9$	$9$	$23.284$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$6$	$0$	$-$	$3^{3}$	$\mathrm{SU}(2)$	$q+(1-\beta _{2})q^{5}+\beta _{6}q^{7}+(1+\beta _{3}+\beta _{6}+\cdots)q^{11}+\cdots$
2916.2.a.e	$2916$	$2$	2916.a	1.a	$1$	$12$	$12$	$23.284$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$3^{6}$	$\mathrm{SU}(2)$	$q-\beta _{6}q^{5}+\beta _{3}q^{7}-\beta _{2}q^{11}+(1-\beta _{1}+\cdots)q^{13}+\cdots$
2916.2.e.a	$2916$	$2$	2916.e	9.c	$3$	$6$	$3$	$23.284$	$\Q(\zeta_{18})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-3$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{5}+(\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{7}+\cdots$
2916.2.e.b	$2916$	$2$	2916.e	9.c	$3$	$6$	$3$	$23.284$	$\Q(\zeta_{18})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$3$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\zeta_{18}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{5}+\cdots$
2916.2.e.c	$2916$	$2$	2916.e	9.c	$3$	$18$	$9$	$23.284$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-6$	$0$		$3^{10}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{5}-\beta _{10}+\beta _{13})q^{5}-\beta _{15}q^{7}+\cdots$
2916.2.e.d	$2916$	$2$	2916.e	9.c	$3$	$18$	$9$	$23.284$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$6$	$0$		$3^{10}$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{5}+\beta _{10}-\beta _{13})q^{5}-\beta _{15}q^{7}+\cdots$
2916.2.e.e	$2916$	$2$	2916.e	9.c	$3$	$24$	$12$	$23.284$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{3}]$
2916.3.c.a	$2916$	$3$	2916.c	3.b	$2$	$36$	$36$	$79.455$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2916.3.c.b	$2916$	$3$	2916.c	3.b	$2$	$36$	$36$	$79.455$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.