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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 (24 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2014.2.a.a	$2014$	$2$	2014.a	1.a	$1$	$1$	$1$	$16.082$	$\Q$	None	✓	$1$	$1$	$-1$	$-2$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}-3q^{5}+2q^{6}-2q^{7}+\cdots$
2014.2.a.b	$2014$	$2$	2014.a	1.a	$1$	$1$	$1$	$16.082$	$\Q$	None	✓	$1$	$0$	$-1$	$2$	$2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}+2q^{5}-2q^{6}+3q^{7}+\cdots$
2014.2.a.c	$2014$	$2$	2014.a	1.a	$1$	$1$	$1$	$16.082$	$\Q$	None	✓	$1$	$0$	$1$	$2$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{5}+2q^{6}-q^{7}+\cdots$
2014.2.a.d	$2014$	$2$	2014.a	1.a	$1$	$2$	$2$	$16.082$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$2$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}+q^{4}-\beta q^{5}+(1+\beta )q^{6}+\cdots$
2014.2.a.e	$2014$	$2$	2014.a	1.a	$1$	$6$	$6$	$16.082$	6.6.1397493.1	None	✓	$1$	$1$	$-6$	$0$	$-3$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(\beta _{2}+\beta _{3}+\beta _{5})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots$
2014.2.a.f	$2014$	$2$	2014.a	1.a	$1$	$7$	$7$	$16.082$	7.7.171553549.1	None	✓	$1$	$1$	$7$	$-2$	$-8$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-\beta _{1}+\beta _{4})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots$
2014.2.a.g	$2014$	$2$	2014.a	1.a	$1$	$8$	$8$	$16.082$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-8$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{5}q^{5}+\beta _{1}q^{6}+\cdots$
2014.2.a.h	$2014$	$2$	2014.a	1.a	$1$	$8$	$8$	$16.082$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$8$	$-4$	$-3$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{2}q^{3}+q^{4}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
2014.2.a.i	$2014$	$2$	2014.a	1.a	$1$	$9$	$9$	$16.082$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$9$	$-2$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{7}q^{5}-\beta _{1}q^{6}+\cdots$
2014.2.a.j	$2014$	$2$	2014.a	1.a	$1$	$11$	$11$	$16.082$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$-11$	$0$	$1$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{8}q^{5}+\beta _{1}q^{6}+\cdots$
2014.2.a.k	$2014$	$2$	2014.a	1.a	$1$	$11$	$11$	$16.082$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$11$	$4$	$3$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots$
2014.2.a.l	$2014$	$2$	2014.a	1.a	$1$	$12$	$12$	$16.082$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$-12$	$-4$	$6$	$-2$	$-$	$3^{2}$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}+\beta _{1}q^{6}+\cdots$
2014.2.b.a	$2014$	$2$	2014.b	53.b	$2$	$2$	$2$	$16.082$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}+iq^{5}-4q^{7}-iq^{8}+\cdots$
2014.2.b.b	$2014$	$2$	2014.b	53.b	$2$	$6$	$6$	$16.082$	6.0.62094400.1	None		$2$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-q^{4}+\beta _{4}q^{5}+(1+\beta _{2})q^{7}+\cdots$
2014.2.b.c	$2014$	$2$	2014.b	53.b	$2$	$30$	$30$	$16.082$		None		$2$	$0$	$0$	$0$	$0$	$6$			$\mathrm{SU}(2)[C_{2}]$
2014.2.b.d	$2014$	$2$	2014.b	53.b	$2$	$44$	$44$	$16.082$		None		$2$	$0$	$0$	$0$	$0$	$-14$			$\mathrm{SU}(2)[C_{2}]$
2014.4.a.a	$2014$	$4$	2014.a	1.a	$1$	$26$	$26$	$118.830$		None	✓	$1$	$1$	$-52$	$4$	$-30$	$27$	$-$		$\mathrm{SU}(2)$
2014.4.a.b	$2014$	$4$	2014.a	1.a	$1$	$26$	$26$	$118.830$		None	✓	$1$	$1$	$52$	$-16$	$-50$	$-35$	$-$		$\mathrm{SU}(2)$
2014.4.a.c	$2014$	$4$	2014.a	1.a	$1$	$28$	$28$	$118.830$		None	✓	$1$	$1$	$-56$	$-2$	$-14$	$-12$	$-$		$\mathrm{SU}(2)$
2014.4.a.d	$2014$	$4$	2014.a	1.a	$1$	$28$	$28$	$118.830$		None	✓	$1$	$1$	$56$	$-10$	$-24$	$-74$	$-$		$\mathrm{SU}(2)$
2014.4.a.e	$2014$	$4$	2014.a	1.a	$1$	$31$	$31$	$118.830$		None	✓	$1$	$0$	$-62$	$-2$	$-14$	$-61$	$+$		$\mathrm{SU}(2)$
2014.4.a.f	$2014$	$4$	2014.a	1.a	$1$	$31$	$31$	$118.830$		None	✓	$1$	$0$	$62$	$14$	$6$	$45$	$+$		$\mathrm{SU}(2)$
2014.4.a.g	$2014$	$4$	2014.a	1.a	$1$	$32$	$32$	$118.830$		None	✓	$1$	$0$	$-64$	$4$	$40$	$6$	$+$		$\mathrm{SU}(2)$
2014.4.a.h	$2014$	$4$	2014.a	1.a	$1$	$32$	$32$	$118.830$		None	✓	$1$	$0$	$64$	$8$	$50$	$112$	$+$		$\mathrm{SU}(2)$

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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.