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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

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

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (20 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	7	127	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6223.2.a.a	$6223$	$2$	6223.a	1.a	$1$	$1$	$1$	$49.691$	$\Q$	None	✓	✓			6223.2.a.a	$1$	$0$	$1$	$0$	$-2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-2q^{5}-3q^{8}-3q^{9}-2q^{10}+\cdots$
6223.2.a.b	$6223$	$2$	6223.a	1.a	$1$	$1$	$1$	$49.691$	$\Q$	None	✓	✓			6223.2.a.a	$1$	$0$	$1$	$0$	$2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{5}-3q^{8}-3q^{9}+2q^{10}+\cdots$
6223.2.a.c	$6223$	$2$	6223.a	1.a	$1$	$2$	$2$	$49.691$	$\Q(\sqrt{5}) $	None	✓				889.2.f.a	$1$	$1$	$3$	$-4$	$3$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-2q^{3}+3\beta q^{4}+(2-\beta )q^{5}+\cdots$
6223.2.a.d	$6223$	$2$	6223.a	1.a	$1$	$2$	$2$	$49.691$	$\Q(\sqrt{5}) $	None	✓				889.2.f.a	$1$	$0$	$3$	$4$	$-3$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+2q^{3}+3\beta q^{4}+(-2+\beta )q^{5}+\cdots$
6223.2.a.e	$6223$	$2$	6223.a	1.a	$1$	$3$	$3$	$49.691$	$\Q(\zeta_{18})^+$	None	✓				127.2.a.a	$1$	$0$	$-3$	$3$	$6$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots$
6223.2.a.f	$6223$	$2$	6223.a	1.a	$1$	$4$	$4$	$49.691$	4.4.3981.1	None	✓				889.2.f.b	$1$	$0$	$2$	$-1$	$3$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{3})q^{2}-\beta _{1}q^{3}+(1-\beta _{2})q^{4}+\cdots$
6223.2.a.g	$6223$	$2$	6223.a	1.a	$1$	$4$	$4$	$49.691$	4.4.3981.1	None	✓				889.2.f.b	$1$	$1$	$2$	$1$	$-3$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{3})q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}+\cdots$
6223.2.a.h	$6223$	$2$	6223.a	1.a	$1$	$7$	$7$	$49.691$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓				127.2.a.b	$1$	$1$	$2$	$-3$	$-8$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1+\beta _{2}-\beta _{3}-\beta _{5}-\beta _{6})q^{3}+\cdots$
6223.2.a.i	$6223$	$2$	6223.a	1.a	$1$	$12$	$12$	$49.691$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓				889.2.a.a	$1$	$1$	$-7$	$4$	$7$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+\beta _{10}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
6223.2.a.j	$6223$	$2$	6223.a	1.a	$1$	$15$	$15$	$49.691$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓				889.2.a.b	$1$	$1$	$0$	$-4$	$-7$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots$
6223.2.a.k	$6223$	$2$	6223.a	1.a	$1$	$16$	$16$	$49.691$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓				889.2.a.c	$1$	$0$	$-2$	$4$	$9$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
6223.2.a.l	$6223$	$2$	6223.a	1.a	$1$	$20$	$20$	$49.691$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓				889.2.a.d	$1$	$0$	$8$	$0$	$-3$	$0$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}+\beta _{16}q^{5}+\cdots$
6223.2.a.m	$6223$	$2$	6223.a	1.a	$1$	$26$	$26$	$49.691$		None	✓	✓			6223.2.a.m	$2$	$1$	$-8$	$0$	$0$	$0$	$-$	$-$	$+$		$\mathrm{SU}(2)$
6223.2.a.n	$6223$	$2$	6223.a	1.a	$1$	$34$	$34$	$49.691$		None	✓	✓			6223.2.a.n	$2$	$0$	$6$	$0$	$0$	$0$	$-$	$+$	$-$		$\mathrm{SU}(2)$
6223.2.a.o	$6223$	$2$	6223.a	1.a	$1$	$38$	$38$	$49.691$		None	✓		✓		889.2.f.c	$1$	$1$	$-2$	$-11$	$-16$	$0$	$-$	$-$	$+$		$\mathrm{SU}(2)$
6223.2.a.p	$6223$	$2$	6223.a	1.a	$1$	$38$	$38$	$49.691$		None	✓				889.2.f.c	$1$	$0$	$-2$	$11$	$16$	$0$	$+$	$-$	$-$		$\mathrm{SU}(2)$
6223.2.a.q	$6223$	$2$	6223.a	1.a	$1$	$40$	$40$	$49.691$		None	✓				889.2.f.d	$1$	$1$	$-3$	$-6$	$-24$	$0$	$+$	$+$	$+$		$\mathrm{SU}(2)$
6223.2.a.r	$6223$	$2$	6223.a	1.a	$1$	$40$	$40$	$49.691$		None	✓		✓		889.2.f.d	$1$	$0$	$-3$	$6$	$24$	$0$	$-$	$+$	$-$		$\mathrm{SU}(2)$
6223.2.a.s	$6223$	$2$	6223.a	1.a	$1$	$54$	$54$	$49.691$		None	✓	✓	✓		6223.2.a.s	$2$	$1$	$-14$	$0$	$0$	$0$	$+$	$+$	$+$		$\mathrm{SU}(2)$
6223.2.a.t	$6223$	$2$	6223.a	1.a	$1$	$74$	$74$	$49.691$		None	✓	✓	✓		6223.2.a.t	$2$	$0$	$18$	$0$	$0$	$0$	$+$	$-$	$-$		$\mathrm{SU}(2)$

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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.