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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

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Results (1-50 of 157 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
558.2.a.a	$558$	$2$	558.a	1.a	$1$	$1$	$1$	$4.456$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots$
558.2.a.b	$558$	$2$	558.a	1.a	$1$	$1$	$1$	$4.456$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-3q^{11}+\cdots$
558.2.a.c	$558$	$2$	558.a	1.a	$1$	$1$	$1$	$4.456$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+2q^{13}+\cdots$
558.2.a.d	$558$	$2$	558.a	1.a	$1$	$1$	$1$	$4.456$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$3$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}-4q^{7}-q^{8}-3q^{10}+\cdots$
558.2.a.e	$558$	$2$	558.a	1.a	$1$	$1$	$1$	$4.456$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}-4q^{7}+q^{8}-3q^{10}+\cdots$
558.2.a.f	$558$	$2$	558.a	1.a	$1$	$1$	$1$	$4.456$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}-2q^{7}+q^{8}-3q^{10}+\cdots$
558.2.a.g	$558$	$2$	558.a	1.a	$1$	$1$	$1$	$4.456$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+3q^{11}+\cdots$
558.2.a.h	$558$	$2$	558.a	1.a	$1$	$1$	$1$	$4.456$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots$
558.2.a.i	$558$	$2$	558.a	1.a	$1$	$2$	$2$	$4.456$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$-2$	$0$	$-3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta )q^{5}+(2-2\beta )q^{7}+\cdots$
558.2.a.j	$558$	$2$	558.a	1.a	$1$	$2$	$2$	$4.456$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2\beta q^{5}+2q^{7}+q^{8}+2\beta q^{10}+\cdots$
558.2.c.a	$558$	$2$	558.c	93.c	$2$	$8$	$8$	$4.456$	8.0.3557883904.7	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}-q^{4}-\beta _{5}q^{5}-\beta _{1}q^{7}-\beta _{5}q^{8}+\cdots$
558.2.e.a	$558$	$2$	558.e	31.c	$3$	$2$	$1$	$4.456$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-2$	$0$	$-2$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+q^{4}-2\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots$
558.2.e.b	$558$	$2$	558.e	31.c	$3$	$2$	$1$	$4.456$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-2$	$0$	$1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+q^{4}+\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+\cdots$
558.2.e.c	$558$	$2$	558.e	31.c	$3$	$2$	$1$	$4.456$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$0$	$-3$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+q^{4}-3\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots$
558.2.e.d	$558$	$2$	558.e	31.c	$3$	$2$	$1$	$4.456$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$2$	$0$	$2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+q^{4}+2\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots$
558.2.e.e	$558$	$2$	558.e	31.c	$3$	$4$	$2$	$4.456$	$\Q(\sqrt{2}, \sqrt{-3})$	None		$2$	$0$	$-4$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+q^{4}+2\beta _{1}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
558.2.e.f	$558$	$2$	558.e	31.c	$3$	$4$	$2$	$4.456$	$\Q(\sqrt{-3}, \sqrt{19})$	None		$2$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+q^{4}+\beta _{1}q^{7}+q^{8}+(\beta _{1}+2\beta _{2}+\cdots)q^{11}+\cdots$
558.2.e.g	$558$	$2$	558.e	31.c	$3$	$6$	$3$	$4.456$	6.0.15759792.1	None		$2$	$0$	$-6$	$0$	$-2$	$-1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{2}+q^{4}+(\beta _{3}-\beta _{4})q^{5}+(\beta _{1}-\beta _{5})q^{7}+\cdots$
558.2.e.h	$558$	$2$	558.e	31.c	$3$	$6$	$3$	$4.456$	6.0.15759792.1	None		$2$	$0$	$6$	$0$	$2$	$-1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+q^{4}+(-\beta _{3}+\beta _{4})q^{5}+(\beta _{1}-\beta _{5})q^{7}+\cdots$
558.2.f.a	$558$	$2$	558.f	9.c	$3$	$2$	$1$	$4.456$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$-3$	$0$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
558.2.f.b	$558$	$2$	558.f	9.c	$3$	$2$	$1$	$4.456$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$3$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
558.2.f.c	$558$	$2$	558.f	9.c	$3$	$4$	$2$	$4.456$	$\Q(\zeta_{12})$	None		$2$	$0$	$2$	$0$	$2$	$6$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{12}q^{2}-\zeta_{12}^{2}q^{3}+(-1+\zeta_{12}+\cdots)q^{4}+\cdots$
558.2.f.d	$558$	$2$	558.f	9.c	$3$	$8$	$4$	$4.456$	8.0.142635249.1	None		$2$	$0$	$-4$	$-1$	$1$	$3$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{2}q^{2}-\beta _{4}q^{3}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
558.2.f.e	$558$	$2$	558.f	9.c	$3$	$8$	$4$	$4.456$	8.0.142635249.1	None		$2$	$0$	$4$	$-1$	$-3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{4})q^{2}+(\beta _{3}+\beta _{6})q^{3}-\beta _{4}q^{4}+\cdots$
558.2.f.f	$558$	$2$	558.f	9.c	$3$	$16$	$8$	$4.456$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-8$	$5$	$-1$	$-10$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{7})q^{2}+(-\beta _{1}+\beta _{12})q^{3}+\cdots$
558.2.f.g	$558$	$2$	558.f	9.c	$3$	$20$	$10$	$4.456$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$10$	$-1$	$3$	$-7$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{9}q^{2}-\beta _{1}q^{3}+(-1+\beta _{9})q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots$
558.2.g.a	$558$	$2$	558.g	279.e	$3$	$32$	$16$	$4.456$		None		$2$	$0$	$-16$	$4$	$-1$	$1$			$\mathrm{SU}(2)[C_{3}]$
558.2.g.b	$558$	$2$	558.g	279.e	$3$	$32$	$16$	$4.456$		None		$2$	$0$	$16$	$4$	$-1$	$1$			$\mathrm{SU}(2)[C_{3}]$
558.2.h.a	$558$	$2$	558.h	279.g	$3$	$32$	$16$	$4.456$		None		$2$	$0$	$-16$	$-2$	$2$	$-2$			$\mathrm{SU}(2)[C_{3}]$
558.2.h.b	$558$	$2$	558.h	279.g	$3$	$32$	$16$	$4.456$		None		$2$	$0$	$16$	$-2$	$2$	$-2$			$\mathrm{SU}(2)[C_{3}]$
558.2.i.a	$558$	$2$	558.i	31.d	$5$	$4$	$1$	$4.456$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$0$	$-6$	$-5$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+(-2-\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
558.2.i.b	$558$	$2$	558.i	31.d	$5$	$4$	$1$	$4.456$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$0$	$-2$	$7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+(\zeta_{10}^{2}-\zeta_{10}^{3})q^{5}+\cdots$
558.2.i.c	$558$	$2$	558.i	31.d	$5$	$4$	$1$	$4.456$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$0$	$4$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+(-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{5}+\cdots$
558.2.i.d	$558$	$2$	558.i	31.d	$5$	$4$	$1$	$4.456$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$0$	$8$	$4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+2q^{5}+(\zeta_{10}+\cdots)q^{7}+\cdots$
558.2.i.e	$558$	$2$	558.i	31.d	$5$	$4$	$1$	$4.456$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$0$	$-8$	$4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}-2q^{5}+(\zeta_{10}+\cdots)q^{7}+\cdots$
558.2.i.f	$558$	$2$	558.i	31.d	$5$	$4$	$1$	$4.456$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$0$	$6$	$-5$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+(2+\zeta_{10}^{2}-\zeta_{10}^{3})q^{5}+\cdots$
558.2.i.g	$558$	$2$	558.i	31.d	$5$	$8$	$2$	$4.456$	8.0.1903140625.1	None		$2$	$0$	$-2$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{2}q^{2}-\beta _{3}q^{4}+(-1+\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots$
558.2.i.h	$558$	$2$	558.i	31.d	$5$	$8$	$2$	$4.456$	8.0.9240015625.1	None		$2$	$0$	$2$	$0$	$-2$	$-7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{5}q^{2}+(-1+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots$
558.2.i.i	$558$	$2$	558.i	31.d	$5$	$8$	$2$	$4.456$	8.0.511890625.1	None		$2$	$0$	$2$	$0$	$4$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{2}q^{2}+\beta _{4}q^{4}+(\beta _{1}-\beta _{5}+\beta _{6})q^{5}+\cdots$
558.2.j.a	$558$	$2$	558.j	279.o	$6$	$64$	$32$	$4.456$		None		$2$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{6}]$
558.2.p.a	$558$	$2$	558.p	93.g	$6$	$24$	$12$	$4.456$		None		$4$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{6}]$
558.2.q.a	$558$	$2$	558.q	279.s	$6$	$64$	$32$	$4.456$		None		$4$	$0$	$0$	$0$	$12$	$-4$			$\mathrm{SU}(2)[C_{6}]$
558.2.t.a	$558$	$2$	558.t	279.r	$6$	$64$	$32$	$4.456$		None		$2$	$0$	$0$	$0$	$6$	$2$			$\mathrm{SU}(2)[C_{6}]$
558.2.v.a	$558$	$2$	558.v	93.k	$10$	$32$	$8$	$4.456$		None		$4$	$0$	$0$	$0$	$0$	$20$			$\mathrm{SU}(2)[C_{10}]$
558.2.y.a	$558$	$2$	558.y	279.aa	$15$	$128$	$16$	$4.456$		None		$2$	$0$	$-16$	$-4$	$1$	$-1$			$\mathrm{SU}(2)[C_{15}]$
558.2.y.b	$558$	$2$	558.y	279.aa	$15$	$128$	$16$	$4.456$		None		$2$	$0$	$16$	$-4$	$1$	$-1$			$\mathrm{SU}(2)[C_{15}]$
558.2.z.a	$558$	$2$	558.z	279.z	$15$	$128$	$16$	$4.456$		None		$4$	$0$	$-16$	$2$	$-2$	$2$			$\mathrm{SU}(2)[C_{15}]$
558.2.z.b	$558$	$2$	558.z	279.z	$15$	$128$	$16$	$4.456$		None		$4$	$0$	$16$	$2$	$-2$	$2$			$\mathrm{SU}(2)[C_{15}]$
558.2.ba.a	$558$	$2$	558.ba	31.g	$15$	$8$	$1$	$4.456$	$\Q(\zeta_{15})$	None		$2$	$0$	$-2$	$0$	$-7$	$14$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q+\zeta_{15}^{6}q^{2}+(-\zeta_{15}^{2}-\zeta_{15}^{7})q^{4}+\cdots$
558.2.ba.b	$558$	$2$	558.ba	31.g	$15$	$8$	$1$	$4.456$	$\Q(\zeta_{15})$	None		$2$	$0$	$-2$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q+\zeta_{15}^{6}q^{2}+(-\zeta_{15}^{2}-\zeta_{15}^{7})q^{4}+\cdots$

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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.