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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 (19 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
2668.1.b.a	$2668$	$1$	2668.b	667.b	$2$	$1$	$1$	$1.332$	$\Q$	$D_{3}$	$\Q(\sqrt{-667}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{9}-2q^{11}-q^{13}+q^{17}+q^{19}+\cdots$
2668.1.b.b	$2668$	$1$	2668.b	667.b	$2$	$1$	$1$	$1.332$	$\Q$	$D_{3}$	$\Q(\sqrt{-667}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{9}+2q^{11}-q^{13}-q^{17}-q^{19}+\cdots$
2668.1.b.c	$2668$	$1$	2668.b	667.b	$2$	$2$	$2$	$1.332$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-667}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{9}+q^{13}-\beta q^{17}+\beta q^{19}-q^{23}+\cdots$
2668.1.l.a	$2668$	$1$	2668.l	2668.l	$4$	$2$	$1$	$1.332$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-2$	$-2$	$0$	$0$		$1$		$q-q^{2}+(-1+i)q^{3}+q^{4}+(1-i)q^{6}+\cdots$
2668.1.l.b	$2668$	$1$	2668.l	2668.l	$4$	$2$	$1$	$1.332$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q-iq^{2}+(1-i)q^{3}-q^{4}+(-1-i+\cdots)q^{6}+\cdots$
2668.1.l.c	$2668$	$1$	2668.l	2668.l	$4$	$4$	$2$	$1.332$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{3}-\zeta_{12}^{4}q^{4}+\cdots$
2668.1.l.d	$2668$	$1$	2668.l	2668.l	$4$	$4$	$2$	$1.332$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$2$	$2$	$0$	$0$		$1$		$q+\zeta_{12}^{2}q^{2}+(-\zeta_{12}+\zeta_{12}^{2})q^{3}+\zeta_{12}^{4}q^{4}+\cdots$
2668.1.bc.a	$2668$	$1$	2668.bc	2668.ac	$28$	$12$	$1$	$1.332$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-\zeta_{28}^{7}q^{2}+(\zeta_{28}^{4}+\zeta_{28}^{13})q^{3}-q^{4}+\cdots$
2668.1.bc.b	$2668$	$1$	2668.bc	2668.ac	$28$	$12$	$1$	$1.332$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$2$	$2$	$0$	$0$		$1$		$q+\zeta_{28}^{2}q^{2}+(-\zeta_{28}^{4}-\zeta_{28}^{13})q^{3}+\cdots$
2668.1.bc.c	$2668$	$1$	2668.bc	2668.ac	$28$	$24$	$2$	$1.332$	$\Q(\zeta_{84})$	$D_{84}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-2$	$-2$	$0$	$0$		$1$		$q-\zeta_{84}^{4}q^{2}+(\zeta_{84}^{5}+\zeta_{84}^{22})q^{3}+\zeta_{84}^{8}q^{4}+\cdots$
2668.1.bc.d	$2668$	$1$	2668.bc	2668.ac	$28$	$24$	$2$	$1.332$	$\Q(\zeta_{84})$	$D_{84}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\zeta_{84}^{35}q^{2}+(\zeta_{84}^{5}-\zeta_{84}^{22})q^{3}+\cdots$
2668.2.a.a	$2668$	$2$	2668.a	1.a	$1$	$1$	$1$	$21.304$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}+q^{9}-2q^{13}-4q^{15}+\cdots$
2668.2.a.b	$2668$	$2$	2668.a	1.a	$1$	$10$	$10$	$21.304$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(\beta _{5}+\beta _{7}-\beta _{8})q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots$
2668.2.a.c	$2668$	$2$	2668.a	1.a	$1$	$12$	$12$	$21.304$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$5$	$0$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{4}q^{5}+\beta _{8}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots$
2668.2.a.d	$2668$	$2$	2668.a	1.a	$1$	$13$	$13$	$21.304$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-7$	$0$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}-\beta _{4}q^{5}-\beta _{7}q^{7}+(1+\cdots)q^{9}+\cdots$
2668.2.a.e	$2668$	$2$	2668.a	1.a	$1$	$14$	$14$	$21.304$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$11$	$-2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+\beta _{8}q^{5}-\beta _{5}q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots$
2668.2.e.a	$2668$	$2$	2668.e	29.b	$2$	$2$	$2$	$21.304$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$8$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{3}+4q^{5}+4q^{7}-q^{9}-4iq^{11}+\cdots$
2668.2.e.b	$2668$	$2$	2668.e	29.b	$2$	$26$	$26$	$21.304$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-10$	$2$			$\mathrm{SU}(2)[C_{2}]$
2668.2.e.c	$2668$	$2$	2668.e	29.b	$2$	$28$	$28$	$21.304$		$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$-2$			$\mathrm{SU}(2)[C_{2}]$

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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.