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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is twist minimal	Is self-dual

$Nk^2$	Coefficient ring index	Coefficient ring gens.	Projective image	Projective image type

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Results (20 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Minimal twist	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	Twist minimal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3645.1.n.a	$3645$	$1$	3645.n	135.n	$18$	$6$	$1$	$1.819$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-15}) $	None			1215.1.d.a	$4$	$0$	$-6$	$0$	$0$	$0$		$1$		$q+(-1+\zeta_{18}^{7})q^{2}+(1-\zeta_{18}^{5}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots$
3645.1.n.b	$3645$	$1$	3645.n	135.n	$18$	$6$	$1$	$1.819$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-15}) $	None			1215.1.d.a	$4$	$0$	$-3$	$0$	$0$	$0$		$1$		$q+(-\zeta_{18}^{3}+\zeta_{18}^{4})q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots$
3645.1.n.c	$3645$	$1$	3645.n	135.n	$18$	$6$	$1$	$1.819$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-15}) $	None			1215.1.d.a	$4$	$0$	$-3$	$0$	$0$	$0$		$1$		$q+(-\zeta_{18}+\zeta_{18}^{6})q^{2}+(\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{4}+\cdots$
3645.1.n.d	$3645$	$1$	3645.n	135.n	$18$	$6$	$1$	$1.819$	$\Q(\zeta_{18})$	$D_{3}$	$\Q(\sqrt{-15}) $	None			135.1.d.a	$12$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{8}q^{2}+\zeta_{18}^{4}q^{5}+\zeta_{18}^{6}q^{8}+\cdots$
3645.1.n.e	$3645$	$1$	3645.n	135.n	$18$	$6$	$1$	$1.819$	$\Q(\zeta_{18})$	$D_{3}$	$\Q(\sqrt{-15}) $	None			135.1.d.a	$12$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{8}q^{2}-\zeta_{18}^{4}q^{5}-\zeta_{18}^{6}q^{8}+\cdots$
3645.1.n.f	$3645$	$1$	3645.n	135.n	$18$	$6$	$1$	$1.819$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-15}) $	None			1215.1.d.a	$4$	$0$	$3$	$0$	$0$	$0$		$1$		$q+(\zeta_{18}^{3}-\zeta_{18}^{4})q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots$
3645.1.n.g	$3645$	$1$	3645.n	135.n	$18$	$6$	$1$	$1.819$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-15}) $	None			1215.1.d.a	$4$	$0$	$3$	$0$	$0$	$0$		$1$		$q+(\zeta_{18}-\zeta_{18}^{6})q^{2}+(\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{4}+\cdots$
3645.1.n.h	$3645$	$1$	3645.n	135.n	$18$	$6$	$1$	$1.819$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-15}) $	None			1215.1.d.a	$4$	$0$	$6$	$0$	$0$	$0$		$1$		$q+(1-\zeta_{18}^{7})q^{2}+(1-\zeta_{18}^{5}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots$
3645.2.a.a	$3645$	$2$	3645.a	1.a	$1$	$3$	$3$	$29.105$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	✓	3645.2.a.a	$1$	$0$	$0$	$0$	$-3$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(-2-2\beta _{2})q^{7}+\cdots$
3645.2.a.b	$3645$	$2$	3645.a	1.a	$1$	$3$	$3$	$29.105$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	✓	3645.2.a.a	$1$	$1$	$0$	$0$	$3$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(-2-2\beta _{2})q^{7}+\cdots$
3645.2.a.c	$3645$	$2$	3645.a	1.a	$1$	$6$	$6$	$29.105$	6.6.3916917.1	$_{}$	None	None	✓	✓	3645.2.a.c	$1$	$1$	$-3$	$0$	$6$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(2+\beta _{2})q^{4}+q^{5}+\cdots$
3645.2.a.d	$3645$	$2$	3645.a	1.a	$1$	$6$	$6$	$29.105$	6.6.3916917.1	$_{}$	None	None	✓	✓	3645.2.a.c	$1$	$0$	$3$	$0$	$-6$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2+\beta _{2})q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots$
3645.2.a.e	$3645$	$2$	3645.a	1.a	$1$	$9$	$9$	$29.105$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓	3645.2.a.e	$1$	$1$	$-3$	$0$	$9$	$-9$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{4}+\beta _{5}+\beta _{7}+\cdots)q^{4}+\cdots$
3645.2.a.f	$3645$	$2$	3645.a	1.a	$1$	$9$	$9$	$29.105$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓	3645.2.a.e	$1$	$0$	$3$	$0$	$-9$	$-9$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{4}+\beta _{5}+\beta _{7}+\cdots)q^{4}+\cdots$
3645.2.a.g	$3645$	$2$	3645.a	1.a	$1$	$15$	$15$	$29.105$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓		135.2.k.a	$1$	$1$	$-3$	$0$	$15$	$-12$	$+$	$3^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1-\beta _{14})q^{7}+\cdots$
3645.2.a.h	$3645$	$2$	3645.a	1.a	$1$	$15$	$15$	$29.105$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓		135.2.k.a	$1$	$1$	$3$	$0$	$-15$	$-12$	$+$	$3^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(-1-\beta _{14})q^{7}+\cdots$
3645.2.a.i	$3645$	$2$	3645.a	1.a	$1$	$18$	$18$	$29.105$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None	✓	✓	3645.2.a.i	$1$	$1$	$-6$	$0$	$-18$	$12$	$+$	$3^{5}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots$
3645.2.a.j	$3645$	$2$	3645.a	1.a	$1$	$18$	$18$	$29.105$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None	✓	✓	3645.2.a.i	$1$	$0$	$6$	$0$	$18$	$12$	$-$	$3^{5}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots$
3645.2.a.k	$3645$	$2$	3645.a	1.a	$1$	$21$	$21$	$29.105$		$_{}$	None	None	✓		135.2.k.b	$1$	$0$	$-3$	$0$	$-21$	$12$	$-$		$\mathrm{SU}(2)$
3645.2.a.l	$3645$	$2$	3645.a	1.a	$1$	$21$	$21$	$29.105$		$_{}$	None	None	✓		135.2.k.b	$1$	$0$	$3$	$0$	$21$	$12$	$-$		$\mathrm{SU}(2)$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 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.