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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 53 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
451.1.b.a	$451$	$1$	451.b	451.b	$2$	$1$	$1$	$0.225$	$\Q$	$D_{3}$	$\Q(\sqrt{-451}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$-1$		$1$		$q+q^{4}-q^{5}-q^{7}+q^{9}+q^{11}+2q^{13}+\cdots$
451.1.b.b	$451$	$1$	451.b	451.b	$2$	$1$	$1$	$0.225$	$\Q$	$D_{3}$	$\Q(\sqrt{-451}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$1$		$1$		$q+q^{4}-q^{5}+q^{7}+q^{9}-q^{11}-2q^{13}+\cdots$
451.1.f.a	$451$	$1$	451.f	451.f	$4$	$4$	$2$	$0.225$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+q^{4}-\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots$
451.2.a.a	$451$	$2$	451.a	1.a	$1$	$1$	$1$	$3.601$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-3$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-3q^{5}+4q^{7}-2q^{9}+\cdots$
451.2.a.b	$451$	$2$	451.a	1.a	$1$	$5$	$5$	$3.601$	5.5.36497.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$-4$	$-4$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(-1+\beta _{1}+\beta _{4})q^{3}+(1+\beta _{4})q^{4}+\cdots$
451.2.a.c	$451$	$2$	451.a	1.a	$1$	$5$	$5$	$3.601$	5.5.24217.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-8$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots$
451.2.a.d	$451$	$2$	451.a	1.a	$1$	$10$	$10$	$3.601$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$4$	$0$	$6$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{4}+\cdots)q^{5}+\cdots$
451.2.a.e	$451$	$2$	451.a	1.a	$1$	$12$	$12$	$3.601$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$1$	$13$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{11})q^{5}+\cdots$
451.2.d.a	$451$	$2$	451.d	41.b	$2$	$36$	$36$	$3.601$		$_{}$	None	None		$2$	$0$	$2$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{2}]$
451.2.e.a	$451$	$2$	451.e	41.c	$4$	$68$	$34$	$3.601$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
451.2.g.a	$451$	$2$	451.g	11.c	$5$	$64$	$16$	$3.601$		$_{}$	None	None		$2$	$0$	$-2$	$3$	$1$	$-3$			$\mathrm{SU}(2)[C_{5}]$
451.2.g.b	$451$	$2$	451.g	11.c	$5$	$96$	$24$	$3.601$		$_{}$	None	None		$2$	$0$	$-2$	$-5$	$-7$	$-3$			$\mathrm{SU}(2)[C_{5}]$
451.2.h.a	$451$	$2$	451.h	451.h	$5$	$160$	$40$	$3.601$		$_{}$	None	None		$2$	$0$	$1$	$-7$	$-1$	$-6$			$\mathrm{SU}(2)[C_{5}]$
451.2.i.a	$451$	$2$	451.i	451.i	$5$	$160$	$40$	$3.601$		$_{}$	None	None		$2$	$0$	$1$	$-7$	$-1$	$-1$			$\mathrm{SU}(2)[C_{5}]$
451.2.j.a	$451$	$2$	451.j	451.j	$5$	$160$	$40$	$3.601$		$_{}$	None	None		$2$	$0$	$1$	$-7$	$-6$	$-1$			$\mathrm{SU}(2)[C_{5}]$
451.2.k.a	$451$	$2$	451.k	41.d	$5$	$72$	$18$	$3.601$		$_{}$	None	None		$2$	$0$	$-1$	$-8$	$-6$	$1$			$\mathrm{SU}(2)[C_{5}]$
451.2.k.b	$451$	$2$	451.k	41.d	$5$	$72$	$18$	$3.601$		$_{}$	None	None		$2$	$0$	$-1$	$8$	$-6$	$-1$			$\mathrm{SU}(2)[C_{5}]$
451.2.l.a	$451$	$2$	451.l	451.l	$5$	$160$	$40$	$3.601$		$_{}$	None	None		$2$	$0$	$-14$	$-7$	$-1$	$-1$			$\mathrm{SU}(2)[C_{5}]$
451.2.m.a	$451$	$2$	451.m	451.m	$8$	$160$	$40$	$3.601$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{8}]$
451.2.q.a	$451$	$2$	451.q	41.f	$10$	$144$	$36$	$3.601$		$_{}$	None	None		$2$	$0$	$-2$	$0$	$12$	$0$			$\mathrm{SU}(2)[C_{10}]$
451.2.r.a	$451$	$2$	451.r	451.r	$10$	$160$	$40$	$3.601$		$_{}$	None	None		$2$	$0$	$-3$	$-5$	$-1$	$-5$			$\mathrm{SU}(2)[C_{10}]$
451.2.s.a	$451$	$2$	451.s	451.s	$10$	$160$	$40$	$3.601$		$_{}$	None	None		$2$	$0$	$-3$	$5$	$-1$	$0$			$\mathrm{SU}(2)[C_{10}]$
451.2.t.a	$451$	$2$	451.t	451.t	$10$	$160$	$40$	$3.601$		$_{}$	None	None		$4$	$0$	$-8$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{10}]$
451.2.u.a	$451$	$2$	451.u	451.u	$10$	$160$	$40$	$3.601$		$_{}$	None	None		$2$	$0$	$-3$	$-5$	$-6$	$-5$			$\mathrm{SU}(2)[C_{10}]$
451.2.bf.a	$451$	$2$	451.bf	451.af	$10$	$160$	$40$	$3.601$		$_{}$	None	None		$2$	$0$	$2$	$5$	$-1$	$-5$			$\mathrm{SU}(2)[C_{10}]$
451.2.bg.a	$451$	$2$	451.bg	451.ag	$20$	$320$	$40$	$3.601$		$_{}$	None	None		$2$	$0$	$0$	$-2$	$-10$	$-6$			$\mathrm{SU}(2)[C_{20}]$
451.2.bm.a	$451$	$2$	451.bm	451.am	$20$	$320$	$40$	$3.601$		$_{}$	None	None		$2$	$0$	$-10$	$-12$	$0$	$-6$			$\mathrm{SU}(2)[C_{20}]$
451.2.bn.a	$451$	$2$	451.bn	41.g	$20$	$272$	$34$	$3.601$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{20}]$
451.2.bo.a	$451$	$2$	451.bo	451.ao	$20$	$320$	$40$	$3.601$		$_{}$	None	None		$2$	$0$	$-10$	$-12$	$-10$	$-6$			$\mathrm{SU}(2)[C_{20}]$
451.2.bp.a	$451$	$2$	451.bp	451.ap	$20$	$320$	$40$	$3.601$		$_{}$	None	None		$2$	$0$	$-10$	$-2$	$-10$	$-6$			$\mathrm{SU}(2)[C_{20}]$
451.2.bq.a	$451$	$2$	451.bq	451.aq	$20$	$320$	$40$	$3.601$		$_{}$	None	None		$4$	$0$	$0$	$-2$	$0$	$-6$			$\mathrm{SU}(2)[C_{20}]$
451.2.bt.a	$451$	$2$	451.bt	451.at	$40$	$640$	$40$	$3.601$		$_{}$	None	None		$2$	$0$	$-20$	$-20$	$-12$	$-20$			$\mathrm{SU}(2)[C_{40}]$
451.2.bu.a	$451$	$2$	451.bu	451.au	$40$	$640$	$40$	$3.601$		$_{}$	None	None		$4$	$0$	$-20$	$-20$	$-12$	$-20$			$\mathrm{SU}(2)[C_{40}]$
451.2.bz.a	$451$	$2$	451.bz	451.az	$40$	$640$	$40$	$3.601$		$_{}$	None	None		$2$	$0$	$-20$	$0$	$-12$	$-20$			$\mathrm{SU}(2)[C_{40}]$
451.2.ca.a	$451$	$2$	451.ca	451.ba	$40$	$640$	$40$	$3.601$		$_{}$	None	None		$2$	$0$	$-20$	$0$	$-12$	$-20$			$\mathrm{SU}(2)[C_{40}]$
451.2.cb.a	$451$	$2$	451.cb	451.bb	$40$	$640$	$40$	$3.601$		$_{}$	None	None		$2$	$0$	$-20$	$-20$	$-12$	$-20$			$\mathrm{SU}(2)[C_{40}]$
451.2.cc.a	$451$	$2$	451.cc	451.bc	$40$	$640$	$40$	$3.601$		$_{}$	None	None		$4$	$0$	$0$	$-40$	$-32$	$0$			$\mathrm{SU}(2)[C_{40}]$
451.3.b.a	$451$	$3$	451.b	451.b	$2$	$3$	$3$	$12.289$	3.3.12177.1	$_{}$	$\Q(\sqrt{-451}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{4}+(\beta _{1}+\beta _{2})q^{5}+(2\beta _{1}-\beta _{2})q^{7}+\cdots$
451.3.b.b	$451$	$3$	451.b	451.b	$2$	$3$	$3$	$12.289$	3.3.12177.1	$_{}$	$\Q(\sqrt{-451}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{4}+(\beta _{1}+\beta _{2})q^{5}+(-2\beta _{1}+\beta _{2})q^{7}+\cdots$
451.3.b.c	$451$	$3$	451.b	451.b	$2$	$76$	$76$	$12.289$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{2}]$
451.3.c.a	$451$	$3$	451.c	11.b	$2$	$80$	$80$	$12.289$		$_{}$	None	None		$2$	$0$	$0$	$-2$	$-2$	$0$			$\mathrm{SU}(2)[C_{2}]$
451.4.a.a	$451$	$4$	451.a	1.a	$1$	$21$	$21$	$26.610$		$_{}$	None	None	✓	$1$	$1$	$-6$	$-1$	$-53$	$18$	$-$		$\mathrm{SU}(2)$
451.4.a.b	$451$	$4$	451.a	1.a	$1$	$23$	$23$	$26.610$		$_{}$	None	None	✓	$1$	$1$	$-8$	$-9$	$-51$	$-80$	$-$		$\mathrm{SU}(2)$
451.4.a.c	$451$	$4$	451.a	1.a	$1$	$27$	$27$	$26.610$		$_{}$	None	None	✓	$1$	$0$	$4$	$11$	$47$	$-38$	$+$		$\mathrm{SU}(2)$
451.4.a.d	$451$	$4$	451.a	1.a	$1$	$29$	$29$	$26.610$		$_{}$	None	None	✓	$1$	$0$	$10$	$3$	$49$	$60$	$+$		$\mathrm{SU}(2)$
451.6.a.a	$451$	$6$	451.a	1.a	$1$	$38$	$38$	$72.333$		$_{}$	None	None	✓	$1$	$1$	$-20$	$-43$	$-257$	$-537$	$+$		$\mathrm{SU}(2)$
451.6.a.b	$451$	$6$	451.a	1.a	$1$	$40$	$40$	$72.333$		$_{}$	None	None	✓	$1$	$1$	$-8$	$-12$	$-214$	$149$	$+$		$\mathrm{SU}(2)$
451.6.a.c	$451$	$6$	451.a	1.a	$1$	$44$	$44$	$72.333$		$_{}$	None	None	✓	$1$	$0$	$16$	$-7$	$243$	$443$	$-$		$\mathrm{SU}(2)$
451.6.a.d	$451$	$6$	451.a	1.a	$1$	$46$	$46$	$72.333$		$_{}$	None	None	✓	$1$	$0$	$12$	$24$	$286$	$-243$	$-$		$\mathrm{SU}(2)$
451.8.a.a	$451$	$8$	451.a	1.a	$1$	$54$	$54$	$140.886$		$_{}$	None	None	✓	$1$	$1$	$-24$	$8$	$-1718$	$1901$	$-$		$\mathrm{SU}(2)$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 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.