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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 (20 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
2013.1.bm.a	$2013$	$1$	2013.bm	2013.am	$10$	$4$	$1$	$1.005$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-183}) $	None		$4$	$0$	$-3$	$-1$	$0$	$0$		$1$		$q+(-1+\zeta_{10})q^{2}+\zeta_{10}^{4}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
2013.1.bm.b	$2013$	$1$	2013.bm	2013.am	$10$	$4$	$1$	$1.005$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-183}) $	None		$4$	$0$	$3$	$-1$	$0$	$0$		$1$		$q+(1-\zeta_{10})q^{2}+\zeta_{10}^{4}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
2013.1.bm.c	$2013$	$1$	2013.bm	2013.am	$10$	$8$	$2$	$1.005$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-183}) $	None		$8$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(\zeta_{20}^{5}+\zeta_{20}^{7})q^{2}+\zeta_{20}^{8}q^{3}+(-1+\cdots)q^{4}+\cdots$
2013.1.bm.d	$2013$	$1$	2013.bm	2013.am	$10$	$16$	$4$	$1.005$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-183}) $	None		$8$	$0$	$0$	$4$	$0$	$0$		$1$		$q+(\zeta_{40}^{9}+\zeta_{40}^{15})q^{2}-\zeta_{40}^{16}q^{3}+\cdots$
2013.2.a.a	$2013$	$2$	2013.a	1.a	$1$	$11$	$11$	$16.074$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-4$	$11$	$-13$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots$
2013.2.a.b	$2013$	$2$	2013.a	1.a	$1$	$11$	$11$	$16.074$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-11$	$-1$	$-11$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{8}q^{5}+\cdots$
2013.2.a.c	$2013$	$2$	2013.a	1.a	$1$	$12$	$12$	$16.074$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-7$	$12$	$-7$	$-15$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
2013.2.a.d	$2013$	$2$	2013.a	1.a	$1$	$12$	$12$	$16.074$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$1$	$-12$	$-3$	$-9$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots$
2013.2.a.e	$2013$	$2$	2013.a	1.a	$1$	$13$	$13$	$16.074$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$2$	$-13$	$3$	$11$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots$
2013.2.a.f	$2013$	$2$	2013.a	1.a	$1$	$13$	$13$	$16.074$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$4$	$13$	$7$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
2013.2.a.g	$2013$	$2$	2013.a	1.a	$1$	$13$	$13$	$16.074$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$4$	$13$	$7$	$7$	$-$	$5$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{5}+\cdots)q^{5}+\cdots$
2013.2.a.h	$2013$	$2$	2013.a	1.a	$1$	$14$	$14$	$16.074$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-1$	$-14$	$1$	$9$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots$
2013.4.a.a	$2013$	$4$	2013.a	1.a	$1$	$36$	$36$	$118.771$		$_{}$	None	None	✓	$1$	$1$	$-14$	$108$	$-65$	$-105$	$-$		$\mathrm{SU}(2)$
2013.4.a.b	$2013$	$4$	2013.a	1.a	$1$	$36$	$36$	$118.771$		$_{}$	None	None	✓	$1$	$1$	$2$	$-108$	$-5$	$-63$	$-$		$\mathrm{SU}(2)$
2013.4.a.c	$2013$	$4$	2013.a	1.a	$1$	$37$	$37$	$118.771$		$_{}$	None	None	✓	$1$	$1$	$-8$	$111$	$-35$	$-35$	$-$		$\mathrm{SU}(2)$
2013.4.a.d	$2013$	$4$	2013.a	1.a	$1$	$37$	$37$	$118.771$		$_{}$	None	None	✓	$1$	$1$	$-4$	$-111$	$-15$	$-77$	$-$		$\mathrm{SU}(2)$
2013.4.a.e	$2013$	$4$	2013.a	1.a	$1$	$38$	$38$	$118.771$		$_{}$	None	None	✓	$1$	$0$	$-2$	$-114$	$15$	$63$	$+$		$\mathrm{SU}(2)$
2013.4.a.f	$2013$	$4$	2013.a	1.a	$1$	$38$	$38$	$118.771$		$_{}$	None	None	✓	$1$	$0$	$14$	$114$	$35$	$105$	$+$		$\mathrm{SU}(2)$
2013.4.a.g	$2013$	$4$	2013.a	1.a	$1$	$39$	$39$	$118.771$		$_{}$	None	None	✓	$1$	$0$	$4$	$-117$	$5$	$77$	$+$		$\mathrm{SU}(2)$
2013.4.a.h	$2013$	$4$	2013.a	1.a	$1$	$39$	$39$	$118.771$		$_{}$	None	None	✓	$1$	$0$	$8$	$117$	$65$	$35$	$+$		$\mathrm{SU}(2)$

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