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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 (30 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
1335.1.h.a	$1335$	$1$	1335.h	1335.h	$2$	$3$	$3$	$0.666$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-1335}) $	None	✓	$2$	$0$	$-1$	$-3$	$3$	$1$		$1$		$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
1335.1.h.b	$1335$	$1$	1335.h	1335.h	$2$	$3$	$3$	$0.666$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-1335}) $	None	✓	$2$	$0$	$-1$	$3$	$3$	$-1$		$1$		$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
1335.1.h.c	$1335$	$1$	1335.h	1335.h	$2$	$3$	$3$	$0.666$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-1335}) $	None	✓	$2$	$0$	$1$	$-3$	$-3$	$1$		$1$		$q-\beta _{2}q^{2}-q^{3}+(\beta _{1}-\beta _{2})q^{4}-q^{5}+\cdots$
1335.1.h.d	$1335$	$1$	1335.h	1335.h	$2$	$3$	$3$	$0.666$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-1335}) $	None	✓	$2$	$0$	$1$	$3$	$-3$	$-1$		$1$		$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
1335.1.h.e	$1335$	$1$	1335.h	1335.h	$2$	$4$	$4$	$0.666$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{445}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{3}-q^{4}-\zeta_{8}^{2}q^{5}+(\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots$
1335.2.a.a	$1335$	$2$	1335.a	1.a	$1$	$1$	$1$	$10.660$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+3q^{8}+\cdots$
1335.2.a.b	$1335$	$2$	1335.a	1.a	$1$	$1$	$1$	$10.660$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}+4q^{7}+\cdots$
1335.2.a.c	$1335$	$2$	1335.a	1.a	$1$	$2$	$2$	$10.660$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$-1$	$2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots$
1335.2.a.d	$1335$	$2$	1335.a	1.a	$1$	$3$	$3$	$10.660$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$-2$	$3$	$3$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots$
1335.2.a.e	$1335$	$2$	1335.a	1.a	$1$	$3$	$3$	$10.660$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
1335.2.a.f	$1335$	$2$	1335.a	1.a	$1$	$4$	$4$	$10.660$	4.4.2777.1	$_{}$	None	None	✓	$1$	$1$	$0$	$4$	$-4$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+q^{3}+(1-\beta _{3})q^{4}-q^{5}+\beta _{2}q^{6}+\cdots$
1335.2.a.g	$1335$	$2$	1335.a	1.a	$1$	$6$	$6$	$10.660$	6.6.10407557.1	$_{}$	None	None	✓	$1$	$1$	$-4$	$-6$	$-6$	$1$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}-q^{3}+(2+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
1335.2.a.h	$1335$	$2$	1335.a	1.a	$1$	$9$	$9$	$10.660$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$5$	$-9$	$-9$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
1335.2.a.i	$1335$	$2$	1335.a	1.a	$1$	$10$	$10$	$10.660$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$10$	$-10$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
1335.2.a.j	$1335$	$2$	1335.a	1.a	$1$	$10$	$10$	$10.660$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$-10$	$10$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
1335.2.a.k	$1335$	$2$	1335.a	1.a	$1$	$10$	$10$	$10.660$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$6$	$10$	$10$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
1335.2.c.a	$1335$	$2$	1335.c	5.b	$2$	$44$	$44$	$10.660$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{2}]$
1335.2.c.b	$1335$	$2$	1335.c	5.b	$2$	$44$	$44$	$10.660$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{2}]$
1335.2.e.a	$1335$	$2$	1335.e	445.c	$2$	$44$	$44$	$10.660$		$_{}$	None	None		$2$	$0$	$0$	$-44$	$-2$	$-4$			$\mathrm{SU}(2)[C_{2}]$
1335.2.e.b	$1335$	$2$	1335.e	445.c	$2$	$44$	$44$	$10.660$		$_{}$	None	None		$2$	$0$	$0$	$44$	$-2$	$4$			$\mathrm{SU}(2)[C_{2}]$
1335.2.g.a	$1335$	$2$	1335.g	89.b	$2$	$30$	$30$	$10.660$		$_{}$	None	None		$2$	$0$	$-2$	$0$	$-30$	$0$			$\mathrm{SU}(2)[C_{2}]$
1335.2.g.b	$1335$	$2$	1335.g	89.b	$2$	$30$	$30$	$10.660$		$_{}$	None	None		$2$	$0$	$2$	$0$	$30$	$0$			$\mathrm{SU}(2)[C_{2}]$
1335.4.a.a	$1335$	$4$	1335.a	1.a	$1$	$16$	$16$	$78.768$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-9$	$48$	$80$	$-60$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+3q^{3}+(3-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1335.4.a.b	$1335$	$4$	1335.a	1.a	$1$	$19$	$19$	$78.768$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-2$	$57$	$-95$	$-56$	$-$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+3q^{3}+(3+\beta _{2})q^{4}-5q^{5}+\cdots$
1335.4.a.c	$1335$	$4$	1335.a	1.a	$1$	$19$	$19$	$78.768$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-57$	$95$	$2$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-3q^{3}+(3+\beta _{2})q^{4}+5q^{5}+\cdots$
1335.4.a.d	$1335$	$4$	1335.a	1.a	$1$	$20$	$20$	$78.768$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-13$	$-60$	$-100$	$6$	$-$	$2^{4}\cdot 5$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1335.4.a.e	$1335$	$4$	1335.a	1.a	$1$	$23$	$23$	$78.768$		$_{}$	None	None	✓	$1$	$0$	$5$	$-69$	$-115$	$-22$	$+$		$\mathrm{SU}(2)$
1335.4.a.f	$1335$	$4$	1335.a	1.a	$1$	$26$	$26$	$78.768$		$_{}$	None	None	✓	$1$	$0$	$0$	$78$	$-130$	$84$	$+$		$\mathrm{SU}(2)$
1335.4.a.g	$1335$	$4$	1335.a	1.a	$1$	$26$	$26$	$78.768$		$_{}$	None	None	✓	$1$	$0$	$2$	$-78$	$130$	$-26$	$+$		$\mathrm{SU}(2)$
1335.4.a.h	$1335$	$4$	1335.a	1.a	$1$	$27$	$27$	$78.768$		$_{}$	None	None	✓	$1$	$0$	$9$	$81$	$135$	$80$	$+$		$\mathrm{SU}(2)$

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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.