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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 (48 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
583.1.d.a	$583$	$1$	583.d	583.d	$2$	$1$	$1$	$0.291$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-583}) $	$\Q(\sqrt{53}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{4}+q^{9}+q^{11}+q^{16}+q^{25}-q^{36}+\cdots$
583.1.d.b	$583$	$1$	583.d	583.d	$2$	$2$	$2$	$0.291$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-583}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{2}+q^{4}+q^{9}-q^{11}-q^{16}-\beta q^{18}+\cdots$
583.1.n.a	$583$	$1$	583.n	583.n	$26$	$12$	$1$	$0.291$	$\Q(\zeta_{26})$	$D_{26}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{26}^{6}-\zeta_{26}^{11})q^{3}+\zeta_{26}q^{4}+\cdots$
583.1.o.a	$583$	$1$	583.o	583.o	$26$	$12$	$1$	$0.291$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$-2$	$0$		$1$		$q+(-\zeta_{26}^{9}+\zeta_{26}^{10})q^{3}+\zeta_{26}^{8}q^{4}+\cdots$
583.2.a.a	$583$	$2$	583.a	1.a	$1$	$1$	$1$	$4.655$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$-1$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+4q^{5}-q^{6}+4q^{7}+\cdots$
583.2.a.b	$583$	$2$	583.a	1.a	$1$	$1$	$1$	$4.655$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$1$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+3q^{5}+2q^{6}+\cdots$
583.2.a.c	$583$	$2$	583.a	1.a	$1$	$1$	$1$	$4.655$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$3$	$-3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+2q^{4}-3q^{5}+6q^{6}+\cdots$
583.2.a.d	$583$	$2$	583.a	1.a	$1$	$2$	$2$	$4.655$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+\beta q^{3}+(2-2\beta )q^{4}+\cdots$
583.2.a.e	$583$	$2$	583.a	1.a	$1$	$2$	$2$	$4.655$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-6$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{3}+(-3-\beta )q^{5}+\cdots$
583.2.a.f	$583$	$2$	583.a	1.a	$1$	$6$	$6$	$4.655$	6.6.18123272.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$2$	$-3$	$-11$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}-\beta _{4}q^{3}+(1-\beta _{2}-\beta _{5})q^{4}+\cdots$
583.2.a.g	$583$	$2$	583.a	1.a	$1$	$8$	$8$	$4.655$	8.8.9098775552.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$-8$	$-11$	$-1$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(-1+\beta _{1})q^{3}+(-\beta _{6}+\beta _{7})q^{4}+\cdots$
583.2.a.h	$583$	$2$	583.a	1.a	$1$	$10$	$10$	$4.655$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$-1$	$8$	$3$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
583.2.a.i	$583$	$2$	583.a	1.a	$1$	$12$	$12$	$4.655$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$6$	$10$	$-3$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
583.2.b.a	$583$	$2$	583.b	53.b	$2$	$2$	$2$	$4.655$	$\Q(\sqrt{-7}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{2}+\beta q^{3}-5q^{4}+7q^{6}+2q^{7}+\cdots$
583.2.b.b	$583$	$2$	583.b	53.b	$2$	$2$	$2$	$4.655$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+2iq^{3}+q^{4}-2q^{6}-4q^{7}+\cdots$
583.2.b.c	$583$	$2$	583.b	53.b	$2$	$2$	$2$	$4.655$	$\Q(\sqrt{-7}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}+2q^{4}+\beta q^{5}+2q^{7}-4q^{9}+\cdots$
583.2.b.d	$583$	$2$	583.b	53.b	$2$	$6$	$6$	$4.655$	6.0.2611456.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$8$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{3}-\beta _{5})q^{2}-\beta _{5}q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots$
583.2.b.e	$583$	$2$	583.b	53.b	$2$	$8$	$8$	$4.655$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+\beta _{5}q^{3}+(-1+\beta _{4})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
583.2.b.f	$583$	$2$	583.b	53.b	$2$	$24$	$24$	$4.655$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-6$			$\mathrm{SU}(2)[C_{2}]$
583.2.f.a	$583$	$2$	583.f	583.f	$4$	$4$	$2$	$4.655$	$\Q(i, \sqrt{11})$	$_{}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$6$	$0$		$2$	$\mathrm{U}(1)[D_{4}]$	$q+(\beta _{1}-\beta _{2})q^{3}+2\beta _{1}q^{4}+(2-\beta _{1}-\beta _{3})q^{5}+\cdots$
583.2.f.b	$583$	$2$	583.f	583.f	$4$	$100$	$50$	$4.655$		$_{}$	None	None		$4$	$0$	$0$	$-4$	$-8$	$0$			$\mathrm{SU}(2)[C_{4}]$
583.2.g.a	$583$	$2$	583.g	11.c	$5$	$4$	$1$	$4.655$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$3$	$-3$	$3$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+\cdots$
583.2.g.b	$583$	$2$	583.g	11.c	$5$	$4$	$1$	$4.655$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$4$	$1$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(2-\zeta_{10}+\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+(\zeta_{10}+\cdots)q^{3}+\cdots$
583.2.g.c	$583$	$2$	583.g	11.c	$5$	$96$	$24$	$4.655$		$_{}$	None	None		$2$	$0$	$-5$	$0$	$-6$	$25$			$\mathrm{SU}(2)[C_{5}]$
583.2.g.d	$583$	$2$	583.g	11.c	$5$	$104$	$26$	$4.655$		$_{}$	None	None		$2$	$0$	$-4$	$-2$	$-2$	$-13$			$\mathrm{SU}(2)[C_{5}]$
583.2.j.a	$583$	$2$	583.j	583.j	$10$	$208$	$52$	$4.655$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$6$			$\mathrm{SU}(2)[C_{10}]$
583.2.k.a	$583$	$2$	583.k	53.d	$13$	$252$	$21$	$4.655$		$_{}$	None	None		$2$	$0$	$-1$	$0$	$-2$	$-7$			$\mathrm{SU}(2)[C_{13}]$
583.2.k.b	$583$	$2$	583.k	53.d	$13$	$300$	$25$	$4.655$		$_{}$	None	None		$2$	$0$	$-1$	$-2$	$-8$	$7$			$\mathrm{SU}(2)[C_{13}]$
583.2.l.a	$583$	$2$	583.l	583.l	$20$	$416$	$52$	$4.655$		$_{}$	None	None		$4$	$0$	$-10$	$-8$	$-8$	$0$			$\mathrm{SU}(2)[C_{20}]$
583.2.p.a	$583$	$2$	583.p	53.e	$26$	$240$	$20$	$4.655$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$7$			$\mathrm{SU}(2)[C_{26}]$
583.2.p.b	$583$	$2$	583.p	53.e	$26$	$288$	$24$	$4.655$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-7$			$\mathrm{SU}(2)[C_{26}]$
583.2.q.a	$583$	$2$	583.q	583.q	$52$	$48$	$2$	$4.655$		$_{}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$-6$	$0$			$\mathrm{U}(1)[D_{52}]$
583.2.q.b	$583$	$2$	583.q	583.q	$52$	$1200$	$50$	$4.655$		$_{}$	None	None		$4$	$0$	$0$	$-48$	$-44$	$0$			$\mathrm{SU}(2)[C_{52}]$
583.2.s.a	$583$	$2$	583.s	583.s	$65$	$2496$	$52$	$4.655$		$_{}$	None	None		$4$	$0$	$-37$	$-35$	$-35$	$-45$			$\mathrm{SU}(2)[C_{65}]$
583.2.t.a	$583$	$2$	583.t	583.t	$130$	$2496$	$52$	$4.655$		$_{}$	None	None		$4$	$0$	$-39$	$-39$	$-39$	$-45$			$\mathrm{SU}(2)[C_{130}]$
583.2.x.a	$583$	$2$	583.x	583.x	$260$	$4992$	$52$	$4.655$		$_{}$	None	None		$4$	$0$	$-120$	$-70$	$-70$	$-130$			$\mathrm{SU}(2)[C_{260}]$
583.4.a.a	$583$	$4$	583.a	1.a	$1$	$29$	$29$	$34.398$		$_{}$	None	None	✓	$1$	$1$	$-8$	$-27$	$-55$	$-52$	$-$		$\mathrm{SU}(2)$
583.4.a.b	$583$	$4$	583.a	1.a	$1$	$32$	$32$	$34.398$		$_{}$	None	None	✓	$1$	$1$	$-10$	$-3$	$-55$	$-52$	$-$		$\mathrm{SU}(2)$
583.4.a.c	$583$	$4$	583.a	1.a	$1$	$33$	$33$	$34.398$		$_{}$	None	None	✓	$1$	$0$	$8$	$-3$	$45$	$32$	$+$		$\mathrm{SU}(2)$
583.4.a.d	$583$	$4$	583.a	1.a	$1$	$36$	$36$	$34.398$		$_{}$	None	None	✓	$1$	$0$	$10$	$33$	$85$	$32$	$+$		$\mathrm{SU}(2)$
583.6.a.a	$583$	$6$	583.a	1.a	$1$	$51$	$51$	$93.504$		$_{}$	None	None	✓	$1$	$1$	$-20$	$-108$	$-425$	$-341$	$+$		$\mathrm{SU}(2)$
583.6.a.b	$583$	$6$	583.a	1.a	$1$	$54$	$54$	$93.504$		$_{}$	None	None	✓	$1$	$1$	$-16$	$0$	$-225$	$-341$	$+$		$\mathrm{SU}(2)$
583.6.a.c	$583$	$6$	583.a	1.a	$1$	$55$	$55$	$93.504$		$_{}$	None	None	✓	$1$	$0$	$20$	$0$	$275$	$247$	$-$		$\mathrm{SU}(2)$
583.6.a.d	$583$	$6$	583.a	1.a	$1$	$58$	$58$	$93.504$		$_{}$	None	None	✓	$1$	$0$	$16$	$72$	$275$	$247$	$-$		$\mathrm{SU}(2)$
583.8.a.a	$583$	$8$	583.a	1.a	$1$	$72$	$72$	$182.120$		$_{}$	None	None	✓	$1$	$1$	$-32$	$-216$	$-1375$	$-1529$	$-$		$\mathrm{SU}(2)$
583.8.a.b	$583$	$8$	583.a	1.a	$1$	$75$	$75$	$182.120$		$_{}$	None	None	✓	$1$	$1$	$-40$	$0$	$-1375$	$-1529$	$-$		$\mathrm{SU}(2)$
583.8.a.c	$583$	$8$	583.a	1.a	$1$	$76$	$76$	$182.120$		$_{}$	None	None	✓	$1$	$0$	$32$	$0$	$1125$	$2587$	$+$		$\mathrm{SU}(2)$
583.8.a.d	$583$	$8$	583.a	1.a	$1$	$79$	$79$	$182.120$		$_{}$	None	None	✓	$1$	$0$	$40$	$324$	$2125$	$2587$	$+$		$\mathrm{SU}(2)$

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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.