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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	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
277.2.a.a	$277$	$2$	277.a	1.a	$1$	$1$	$1$	$2.212$	$\Q$	None	✓	$1$	$1$	$1$	$-2$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}-q^{4}+2q^{5}-2q^{6}-4q^{7}+\cdots$
277.2.a.b	$277$	$2$	277.a	1.a	$1$	$3$	$3$	$2.212$	3.3.148.1	None	✓	$1$	$0$	$-1$	$6$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+2q^{3}+(\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
277.2.a.c	$277$	$2$	277.a	1.a	$1$	$9$	$9$	$2.212$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$-6$	$-10$	$-12$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{2}+(-1-\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots$
277.2.a.d	$277$	$2$	277.a	1.a	$1$	$9$	$9$	$2.212$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$4$	$6$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1-\beta _{4}+\beta _{8})q^{3}+(1-\beta _{5}+\cdots)q^{4}+\cdots$
277.2.b.a	$277$	$2$	277.b	277.b	$2$	$22$	$22$	$2.212$		None		$2$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{2}]$
277.2.c.a	$277$	$2$	277.c	277.c	$3$	$2$	$1$	$2.212$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$-1$	$1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}-\zeta_{6}q^{3}-q^{4}+(1-\zeta_{6})q^{5}-\zeta_{6}q^{6}+\cdots$
277.2.c.b	$277$	$2$	277.c	277.c	$3$	$10$	$5$	$2.212$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		$2$	$0$	$-4$	$5$	$4$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{6})q^{2}-\beta _{5}q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots$
277.2.c.c	$277$	$2$	277.c	277.c	$3$	$32$	$16$	$2.212$		None		$2$	$0$	$-2$	$-4$	$-3$	$-9$			$\mathrm{SU}(2)[C_{3}]$
277.2.e.a	$277$	$2$	277.e	277.e	$6$	$2$	$1$	$2.212$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$1$	$3$	$-1$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+2\zeta_{6})q^{2}+\zeta_{6}q^{3}-q^{4}+(1+\cdots)q^{5}+\cdots$
277.2.e.b	$277$	$2$	277.e	277.e	$6$	$12$	$6$	$2.212$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$-6$	$3$	$5$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{4}-\beta _{8})q^{2}+\beta _{5}q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots$
277.2.e.c	$277$	$2$	277.e	277.e	$6$	$32$	$16$	$2.212$		None		$2$	$0$	$0$	$3$	$-12$	$0$			$\mathrm{SU}(2)[C_{6}]$
277.2.g.a	$277$	$2$	277.g	277.g	$23$	$462$	$21$	$2.212$		None		$2$	$0$	$-18$	$-19$	$-15$	$-11$			$\mathrm{SU}(2)[C_{23}]$
277.2.h.a	$277$	$2$	277.h	277.h	$46$	$484$	$22$	$2.212$		None		$2$	$0$	$-23$	$-23$	$-23$	$-27$			$\mathrm{SU}(2)[C_{46}]$
277.2.i.a	$277$	$2$	277.i	277.i	$69$	$968$	$22$	$2.212$		None		$2$	$0$	$-42$	$-46$	$-48$	$-44$			$\mathrm{SU}(2)[C_{69}]$
277.2.k.a	$277$	$2$	277.k	277.k	$138$	$1012$	$23$	$2.212$		None		$2$	$0$	$-46$	$-44$	$-40$	$-50$			$\mathrm{SU}(2)[C_{138}]$
277.3.d.a	$277$	$3$	277.d	277.d	$4$	$92$	$46$	$7.548$		None		$2$	$0$	$-2$	$-4$	$10$	$0$			$\mathrm{SU}(2)[C_{4}]$
277.3.f.a	$277$	$3$	277.f	277.f	$12$	$180$	$45$	$7.548$		None		$2$	$0$	$-10$	$-2$	$-10$	$-6$			$\mathrm{SU}(2)[C_{12}]$
277.3.j.a	$277$	$3$	277.j	277.j	$92$	$2024$	$46$	$7.548$		None		$2$	$0$	$-44$	$-42$	$-56$	$-46$			$\mathrm{SU}(2)[C_{92}]$
277.3.l.a	$277$	$3$	277.l	277.l	$276$	$3960$	$45$	$7.548$		None		$2$	$0$	$-82$	$-90$	$-82$	$-86$			$\mathrm{SU}(2)[C_{276}]$
277.4.a.a	$277$	$4$	277.a	1.a	$1$	$33$	$33$	$16.344$		None	✓	$1$	$1$	$-12$	$-43$	$-61$	$-62$	$-$		$\mathrm{SU}(2)$
277.4.a.b	$277$	$4$	277.a	1.a	$1$	$36$	$36$	$16.344$		None	✓	$1$	$0$	$10$	$41$	$59$	$50$	$+$		$\mathrm{SU}(2)$
277.4.b.a	$277$	$4$	277.b	277.b	$2$	$68$	$68$	$16.344$		None		$2$	$0$	$0$	$-2$	$0$	$36$			$\mathrm{SU}(2)[C_{2}]$
277.6.a.a	$277$	$6$	277.a	1.a	$1$	$56$	$56$	$44.426$		None	✓	$1$	$1$	$-20$	$-136$	$-304$	$-430$	$+$		$\mathrm{SU}(2)$
277.6.a.b	$277$	$6$	277.a	1.a	$1$	$59$	$59$	$44.426$		None	✓	$1$	$0$	$24$	$116$	$296$	$354$	$-$		$\mathrm{SU}(2)$
277.8.a.a	$277$	$8$	277.a	1.a	$1$	$79$	$79$	$86.531$		None	✓	$1$	$1$	$-48$	$-352$	$-1696$	$-2070$	$-$		$\mathrm{SU}(2)$
277.8.a.b	$277$	$8$	277.a	1.a	$1$	$82$	$82$	$86.531$		None	✓	$1$	$0$	$40$	$404$	$1304$	$3418$	$+$		$\mathrm{SU}(2)$
277.10.a.a	$277$	$10$	277.a	1.a	$1$	$102$	$102$	$142.665$		None	✓	$1$	$1$	$-80$	$-1135$	$-6079$	$-24086$	$+$		$\mathrm{SU}(2)$
277.10.a.b	$277$	$10$	277.a	1.a	$1$	$105$	$105$	$142.665$		None	✓	$1$	$0$	$96$	$1133$	$8921$	$14330$	$-$		$\mathrm{SU}(2)$
277.12.a.a	$277$	$12$	277.a	1.a	$1$	$125$	$125$	$212.831$		None	✓	$1$	$1$	$-192$	$-3412$	$-39646$	$-118702$	$-$		$\mathrm{SU}(2)$
277.12.a.b	$277$	$12$	277.a	1.a	$1$	$128$	$128$	$212.831$		None	✓	$1$	$0$	$160$	$3392$	$35354$	$150210$	$+$		$\mathrm{SU}(2)$

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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.