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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 (1-50 of 51 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
731.1.c.a	$731$	$1$	731.c	731.c	$2$	$1$	$1$	$0.365$	$\Q$	$D_{3}$	$\Q(\sqrt{-731}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$2$		$1$		$q-q^{3}+q^{4}-q^{5}+2q^{7}-q^{12}-q^{13}+\cdots$
731.1.c.b	$731$	$1$	731.c	731.c	$2$	$1$	$1$	$0.365$	$\Q$	$D_{2}$	$\Q(\sqrt{-43}) $, $\Q(\sqrt{-731}) $	$\Q(\sqrt{17}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{4}-q^{9}+2q^{13}+q^{16}-q^{17}+\cdots$
731.1.c.c	$731$	$1$	731.c	731.c	$2$	$1$	$1$	$0.365$	$\Q$	$D_{3}$	$\Q(\sqrt{-731}) $	None	✓	$2$	$0$	$0$	$1$	$1$	$-2$		$1$		$q+q^{3}+q^{4}+q^{5}-2q^{7}+q^{12}-q^{13}+\cdots$
731.1.c.d	$731$	$1$	731.c	731.c	$2$	$2$	$2$	$0.365$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-731}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{3}+q^{4}+\beta q^{5}+2q^{9}-\beta q^{12}+\cdots$
731.1.g.a	$731$	$1$	731.g	731.g	$4$	$2$	$1$	$0.365$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{4}-iq^{9}+(-1-i)q^{11}+q^{13}+\cdots$
731.1.l.a	$731$	$1$	731.l	731.l	$8$	$4$	$1$	$0.365$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{9}+(-\zeta_{8}-\zeta_{8}^{2})q^{11}+\cdots$
731.2.a.a	$731$	$2$	731.a	1.a	$1$	$1$	$1$	$5.837$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots$
731.2.a.b	$731$	$2$	731.a	1.a	$1$	$2$	$2$	$5.837$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta )q^{3}-q^{4}+(-1+\beta )q^{5}+\cdots$
731.2.a.c	$731$	$2$	731.a	1.a	$1$	$6$	$6$	$5.837$	6.6.2460365.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-3$	$3$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{3}-\beta _{4})q^{2}+(-1+\beta _{4})q^{3}+(\beta _{4}+\cdots)q^{4}+\cdots$
731.2.a.d	$731$	$2$	731.a	1.a	$1$	$8$	$8$	$5.837$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$1$	$-3$	$-7$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{3}+\beta _{4})q^{3}+(\beta _{2}-\beta _{3})q^{4}+\cdots$
731.2.a.e	$731$	$2$	731.a	1.a	$1$	$19$	$19$	$5.837$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$2$	$5$	$11$	$7$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{16}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
731.2.a.f	$731$	$2$	731.a	1.a	$1$	$21$	$21$	$5.837$		$_{}$	None	None	✓	$1$	$0$	$2$	$-1$	$-3$	$5$	$-$		$\mathrm{SU}(2)$
731.2.d.a	$731$	$2$	731.d	17.b	$2$	$2$	$2$	$5.837$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-q^{4}+\beta q^{5}-3q^{8}+3q^{9}+\beta q^{10}+\cdots$
731.2.d.b	$731$	$2$	731.d	17.b	$2$	$8$	$8$	$5.837$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-2q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{7})q^{7}+\cdots$
731.2.d.c	$731$	$2$	731.d	17.b	$2$	$20$	$20$	$5.837$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$0$		$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}+\beta _{13}q^{3}+(2+\beta _{1})q^{4}+\beta _{10}q^{5}+\cdots$
731.2.d.d	$731$	$2$	731.d	17.b	$2$	$34$	$34$	$5.837$		$_{}$	None	None		$2$	$0$	$-6$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
731.2.e.a	$731$	$2$	731.e	43.c	$3$	$58$	$29$	$5.837$		$_{}$	None	None		$2$	$0$	$-6$	$3$	$-1$	$7$			$\mathrm{SU}(2)[C_{3}]$
731.2.e.b	$731$	$2$	731.e	43.c	$3$	$58$	$29$	$5.837$		$_{}$	None	None		$2$	$0$	$2$	$-5$	$-3$	$-13$			$\mathrm{SU}(2)[C_{3}]$
731.2.f.a	$731$	$2$	731.f	17.c	$4$	$2$	$1$	$5.837$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-iq^{2}+q^{4}+(-1-i)q^{5}+(-2+2i)q^{7}+\cdots$
731.2.f.b	$731$	$2$	731.f	17.c	$4$	$2$	$1$	$5.837$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+iq^{2}+(2+2i)q^{3}+q^{4}+(-2+2i)q^{6}+\cdots$
731.2.f.c	$731$	$2$	731.f	17.c	$4$	$56$	$28$	$5.837$		$_{}$	None	None		$2$	$0$	$0$	$-4$	$-2$	$4$			$\mathrm{SU}(2)[C_{4}]$
731.2.f.d	$731$	$2$	731.f	17.c	$4$	$68$	$34$	$5.837$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{4}]$
731.2.j.a	$731$	$2$	731.j	731.j	$6$	$128$	$64$	$5.837$		$_{}$	None	None		$4$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
731.2.k.a	$731$	$2$	731.k	43.e	$7$	$180$	$30$	$5.837$		$_{}$	None	None		$2$	$0$	$-4$	$-6$	$-6$	$66$			$\mathrm{SU}(2)[C_{7}]$
731.2.k.b	$731$	$2$	731.k	43.e	$7$	$180$	$30$	$5.837$		$_{}$	None	None		$2$	$0$	$0$	$2$	$2$	$-54$			$\mathrm{SU}(2)[C_{7}]$
731.2.m.a	$731$	$2$	731.m	17.d	$8$	$4$	$1$	$5.837$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$1$	$-4$	$-4$	$-8$	$-4$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(-1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots$
731.2.m.b	$731$	$2$	731.m	17.d	$8$	$116$	$29$	$5.837$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
731.2.m.c	$731$	$2$	731.m	17.d	$8$	$128$	$32$	$5.837$		$_{}$	None	None		$2$	$0$	$4$	$4$	$8$	$4$			$\mathrm{SU}(2)[C_{8}]$
731.2.n.a	$731$	$2$	731.n	731.n	$12$	$256$	$64$	$5.837$		$_{}$	None	None		$4$	$0$	$0$	$-6$	$2$	$0$			$\mathrm{SU}(2)[C_{12}]$
731.2.p.a	$731$	$2$	731.p	731.p	$14$	$384$	$64$	$5.837$		$_{}$	None	None		$4$	$0$	$-12$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{14}]$
731.2.s.a	$731$	$2$	731.s	731.s	$16$	$16$	$2$	$5.837$	16.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{16}]$	$q+2\beta _{4}q^{4}-3\beta _{5}q^{9}+(-\beta _{4}-\beta _{6}-\beta _{7}+\cdots)q^{11}+\cdots$
731.2.s.b	$731$	$2$	731.s	731.s	$16$	$496$	$62$	$5.837$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
731.2.u.a	$731$	$2$	731.u	43.g	$21$	$348$	$29$	$5.837$		$_{}$	None	None		$2$	$0$	$-2$	$5$	$3$	$-71$			$\mathrm{SU}(2)[C_{21}]$
731.2.u.b	$731$	$2$	731.u	43.g	$21$	$348$	$29$	$5.837$		$_{}$	None	None		$2$	$0$	$6$	$-3$	$1$	$49$			$\mathrm{SU}(2)[C_{21}]$
731.2.v.a	$731$	$2$	731.v	731.v	$24$	$512$	$64$	$5.837$		$_{}$	None	None		$4$	$0$	$-16$	$-4$	$-12$	$-4$			$\mathrm{SU}(2)[C_{24}]$
731.2.y.a	$731$	$2$	731.y	731.y	$28$	$768$	$64$	$5.837$		$_{}$	None	None		$4$	$0$	$0$	$-14$	$-6$	$-28$			$\mathrm{SU}(2)[C_{28}]$
731.2.z.a	$731$	$2$	731.z	731.z	$42$	$768$	$64$	$5.837$		$_{}$	None	None		$4$	$0$	$-24$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{42}]$
731.2.bd.a	$731$	$2$	731.bd	731.ad	$48$	$1024$	$64$	$5.837$		$_{}$	None	None		$4$	$0$	$0$	$-24$	$-24$	$-24$			$\mathrm{SU}(2)[C_{48}]$
731.2.be.a	$731$	$2$	731.be	731.ae	$56$	$1536$	$64$	$5.837$		$_{}$	None	None		$4$	$0$	$-20$	$-20$	$-28$	$-48$			$\mathrm{SU}(2)[C_{56}]$
731.2.bh.a	$731$	$2$	731.bh	731.ah	$84$	$1536$	$64$	$5.837$		$_{}$	None	None		$4$	$0$	$0$	$-22$	$-30$	$-14$			$\mathrm{SU}(2)[C_{84}]$
731.2.bj.a	$731$	$2$	731.bj	731.aj	$112$	$3072$	$64$	$5.837$		$_{}$	None	None		$4$	$0$	$-56$	$-56$	$-56$	$0$			$\mathrm{SU}(2)[C_{112}]$
731.2.bl.a	$731$	$2$	731.bl	731.al	$168$	$3072$	$64$	$5.837$		$_{}$	None	None		$4$	$0$	$-40$	$-52$	$-44$	$-24$			$\mathrm{SU}(2)[C_{168}]$
731.2.bm.a	$731$	$2$	731.bm	731.am	$336$	$6144$	$64$	$5.837$		$_{}$	None	None		$4$	$0$	$-112$	$-88$	$-88$	$-144$			$\mathrm{SU}(2)[C_{336}]$
731.4.a.a	$731$	$4$	731.a	1.a	$1$	$35$	$35$	$43.130$		$_{}$	None	None	✓	$1$	$1$	$-4$	$2$	$6$	$-26$	$-$		$\mathrm{SU}(2)$
731.4.a.b	$731$	$4$	731.a	1.a	$1$	$37$	$37$	$43.130$		$_{}$	None	None	✓	$1$	$1$	$-4$	$-16$	$-64$	$-74$	$-$		$\mathrm{SU}(2)$
731.4.a.c	$731$	$4$	731.a	1.a	$1$	$47$	$47$	$43.130$		$_{}$	None	None	✓	$1$	$0$	$4$	$2$	$-14$	$58$	$+$		$\mathrm{SU}(2)$
731.4.a.d	$731$	$4$	731.a	1.a	$1$	$49$	$49$	$43.130$		$_{}$	None	None	✓	$1$	$0$	$4$	$20$	$56$	$66$	$+$		$\mathrm{SU}(2)$
731.6.a.a	$731$	$6$	731.a	1.a	$1$	$63$	$63$	$117.241$		$_{}$	None	None	✓	$1$	$1$	$-8$	$-55$	$-271$	$-433$	$+$		$\mathrm{SU}(2)$
731.6.a.b	$731$	$6$	731.a	1.a	$1$	$65$	$65$	$117.241$		$_{}$	None	None	✓	$1$	$1$	$-8$	$-1$	$79$	$-275$	$+$		$\mathrm{SU}(2)$
731.6.a.c	$731$	$6$	731.a	1.a	$1$	$75$	$75$	$117.241$		$_{}$	None	None	✓	$1$	$0$	$8$	$53$	$329$	$547$	$-$		$\mathrm{SU}(2)$

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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.