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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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
335.1.d.a	$335$	$1$	335.d	335.d	$2$	$1$	$1$	$0.167$	$\Q$	$D_{3}$	$\Q(\sqrt{-335}) $	None	✓	$2$	$0$	$-1$	$-1$	$1$	$-1$	$1$		$q-q^{2}-q^{3}+q^{5}+q^{6}-q^{7}+q^{8}+\cdots$
335.1.d.b	$335$	$1$	335.d	335.d	$2$	$1$	$1$	$0.167$	$\Q$	$D_{3}$	$\Q(\sqrt{-335}) $	None	✓	$2$	$0$	$1$	$1$	$-1$	$1$	$1$		$q+q^{2}+q^{3}-q^{5}+q^{6}+q^{7}-q^{8}+\cdots$
335.1.d.c	$335$	$1$	335.d	335.d	$2$	$3$	$3$	$0.167$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-335}) $	None	✓	$2$	$0$	$0$	$0$	$-3$	$0$	$1$		$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$
335.1.d.d	$335$	$1$	335.d	335.d	$2$	$3$	$3$	$0.167$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-335}) $	None	✓	$2$	$0$	$0$	$0$	$3$	$0$	$1$		$q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$
1675.1.b.c	$1675$	$1$	1675.b	67.b	$2$	$2$	$2$	$0.836$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-335}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}+iq^{3}+q^{6}-iq^{7}-iq^{8}+\cdots$
1675.1.b.d	$1675$	$1$	1675.b	67.b	$2$	$6$	$6$	$0.836$	6.0.419904.1	$D_{9}$	$\Q(\sqrt{-335}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(-1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$
2345.1.x.a	$2345$	$1$	2345.x	2345.x	$6$	$18$	$9$	$1.170$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-335}) $	None		$4$	$0$	$0$	$0$	$-9$	$0$	$1$		$q+(-\zeta_{54}^{5}-\zeta_{54}^{13})q^{2}+(-\zeta_{54}^{11}+\cdots)q^{3}+\cdots$
2345.1.x.b	$2345$	$1$	2345.x	2345.x	$6$	$18$	$9$	$1.170$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-335}) $	None		$4$	$0$	$0$	$0$	$9$	$0$	$1$		$q+(\zeta_{54}^{5}+\zeta_{54}^{13})q^{2}+(\zeta_{54}^{11}+\zeta_{54}^{25}+\cdots)q^{3}+\cdots$
2680.1.h.e	$2680$	$1$	2680.h	2680.h	$2$	$2$	$2$	$1.337$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-335}) $, $\Q(\sqrt{-134}) $	$\Q(\sqrt{10}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{2}-iq^{3}-q^{4}+iq^{5}+2q^{6}+\cdots$
2680.1.h.f	$2680$	$1$	2680.h	2680.h	$2$	$4$	$4$	$1.337$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-335}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}+\cdots$
2680.1.h.h	$2680$	$1$	2680.h	2680.h	$2$	$12$	$12$	$1.337$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-335}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{36}q^{2}+(\zeta_{36}^{5}+\zeta_{36}^{13})q^{3}+\zeta_{36}^{2}q^{4}+\cdots$
3015.1.h.a	$3015$	$1$	3015.h	335.d	$2$	$1$	$1$	$1.505$	$\Q$	$D_{3}$	$\Q(\sqrt{-335}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$1$	$1$		$q-q^{2}+q^{5}+q^{7}+q^{8}-q^{10}-2q^{13}+\cdots$
3015.1.h.b	$3015$	$1$	3015.h	335.d	$2$	$1$	$1$	$1.505$	$\Q$	$D_{3}$	$\Q(\sqrt{-335}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$-1$	$1$		$q+q^{2}-q^{5}-q^{7}-q^{8}-q^{10}+2q^{13}+\cdots$
3015.1.h.c	$3015$	$1$	3015.h	335.d	$2$	$3$	$3$	$1.505$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-335}) $	None	✓	$2$	$0$	$0$	$0$	$-3$	$0$	$1$		$q+(-\beta _{1}+\beta _{2})q^{2}+(1-\beta _{1})q^{4}-q^{5}+\cdots$
3015.1.h.d	$3015$	$1$	3015.h	335.d	$2$	$3$	$3$	$1.505$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-335}) $	None	✓	$2$	$0$	$0$	$0$	$3$	$0$	$1$		$q+(\beta _{1}-\beta _{2})q^{2}+(1-\beta _{1})q^{4}+q^{5}+\beta _{1}q^{7}+\cdots$
3015.1.w.a	$3015$	$1$	3015.w	3015.w	$6$	$18$	$9$	$1.505$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-335}) $	None		$4$	$0$	$0$	$0$	$-9$	$0$	$1$		$q+(-\zeta_{54}^{5}-\zeta_{54}^{13})q^{2}+\zeta_{54}^{16}q^{3}+\cdots$
3015.1.w.b	$3015$	$1$	3015.w	3015.w	$6$	$18$	$9$	$1.505$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-335}) $	None		$4$	$0$	$0$	$0$	$9$	$0$	$1$		$q+(\zeta_{54}^{5}+\zeta_{54}^{13})q^{2}-\zeta_{54}^{16}q^{3}+\cdots$
335.3.d.a	$335$	$3$	335.d	335.d	$2$	$9$	$9$	$9.128$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	$\Q(\sqrt{-335}) $	None	✓	$2$	$0$	$0$	$0$	$-45$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}-\beta _{5}q^{3}+(4+\beta _{6}+\beta _{7})q^{4}+\cdots$
335.3.d.b	$335$	$3$	335.d	335.d	$2$	$9$	$9$	$9.128$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	$\Q(\sqrt{-335}) $	None	✓	$2$	$0$	$0$	$0$	$45$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(4+\beta _{6}+\beta _{7})q^{4}+\cdots$

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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.