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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 54 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
644.1.h.a	$644$	$1$	644.h	644.h	$2$	$1$	$1$	$0.321$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-161}) $	$\Q(\sqrt{23}) $	✓	$4$	$0$	$1$	$0$	$0$	$-1$		$1$		$q+q^{2}+q^{4}-q^{7}+q^{8}-q^{9}+2q^{11}+\cdots$
644.1.h.b	$644$	$1$	644.h	644.h	$2$	$1$	$1$	$0.321$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-161}) $	$\Q(\sqrt{23}) $	✓	$4$	$0$	$1$	$0$	$0$	$1$		$1$		$q+q^{2}+q^{4}+q^{7}+q^{8}-q^{9}-2q^{11}+\cdots$
644.1.h.c	$644$	$1$	644.h	644.h	$2$	$2$	$2$	$0.321$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-161}) $	None	✓	$4$	$0$	$-2$	$0$	$0$	$-2$		$1$		$q-q^{2}-\beta q^{3}+q^{4}-\beta q^{5}+\beta q^{6}-q^{7}+\cdots$
644.1.h.d	$644$	$1$	644.h	644.h	$2$	$2$	$2$	$0.321$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-161}) $	None	✓	$4$	$0$	$-2$	$0$	$0$	$2$		$1$		$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}+q^{7}+\cdots$
644.1.r.a	$644$	$1$	644.r	644.r	$22$	$10$	$1$	$0.321$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$-1$		$1$		$q+\zeta_{22}^{6}q^{2}-\zeta_{22}q^{4}-\zeta_{22}^{9}q^{7}-\zeta_{22}^{7}q^{8}+\cdots$
644.1.r.b	$644$	$1$	644.r	644.r	$22$	$10$	$1$	$0.321$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$1$		$1$		$q+\zeta_{22}^{4}q^{2}+\zeta_{22}^{8}q^{4}+\zeta_{22}^{9}q^{7}+\cdots$
644.2.a.a	$644$	$2$	644.a	1.a	$1$	$1$	$1$	$5.142$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}-2q^{11}-3q^{13}+\cdots$
644.2.a.b	$644$	$2$	644.a	1.a	$1$	$1$	$1$	$5.142$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-q^{7}-2q^{9}-2q^{11}+\cdots$
644.2.a.c	$644$	$2$	644.a	1.a	$1$	$5$	$5$	$5.142$	5.5.8580816.1	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$4$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1+\beta _{4})q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
644.2.a.d	$644$	$2$	644.a	1.a	$1$	$5$	$5$	$5.142$	5.5.6963152.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$2$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1-\beta _{2}+\beta _{3})q^{5}-q^{7}+\cdots$
644.2.c.a	$644$	$2$	644.c	92.b	$2$	$36$	$36$	$5.142$		$_{}$	None	None		$2$	$0$	$1$	$0$	$0$	$-36$			$\mathrm{SU}(2)[C_{2}]$
644.2.c.b	$644$	$2$	644.c	92.b	$2$	$36$	$36$	$5.142$		$_{}$	None	None		$2$	$0$	$1$	$0$	$0$	$36$			$\mathrm{SU}(2)[C_{2}]$
644.2.d.a	$644$	$2$	644.d	161.c	$2$	$16$	$16$	$5.142$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{3}+\beta _{2}q^{5}+\beta _{8}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots$
644.2.f.a	$644$	$2$	644.f	28.d	$2$	$4$	$4$	$5.142$	$\Q(i, \sqrt{14})$	$_{}$	None	None		$2$	$0$	$-4$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{2})q^{2}-q^{3}-2\beta _{2}q^{4}-2\beta _{2}q^{5}+\cdots$
644.2.f.b	$644$	$2$	644.f	28.d	$2$	$4$	$4$	$5.142$	$\Q(i, \sqrt{14})$	$_{}$	None	None		$2$	$0$	$-4$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{2})q^{2}+q^{3}-2\beta _{2}q^{4}+2\beta _{2}q^{5}+\cdots$
644.2.f.c	$644$	$2$	644.f	28.d	$2$	$80$	$80$	$5.142$		$_{}$	None	None		$4$	$0$	$8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
644.2.i.a	$644$	$2$	644.i	7.c	$3$	$14$	$7$	$5.142$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-3$	$-2$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{10}q^{3}+(-\beta _{2}-\beta _{11})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots$
644.2.i.b	$644$	$2$	644.i	7.c	$3$	$14$	$7$	$5.142$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$5$	$2$	$4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{1}-\beta _{7})q^{3}+(-\beta _{3}-\beta _{5})q^{5}+\cdots$
644.2.k.a	$644$	$2$	644.k	28.f	$6$	$176$	$88$	$5.142$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
644.2.m.a	$644$	$2$	644.m	161.g	$6$	$32$	$16$	$5.142$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
644.2.p.a	$644$	$2$	644.p	644.p	$6$	$184$	$92$	$5.142$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
644.2.q.a	$644$	$2$	644.q	23.c	$11$	$60$	$6$	$5.142$		$_{}$	None	None		$2$	$0$	$0$	$-4$	$-11$	$6$			$\mathrm{SU}(2)[C_{11}]$
644.2.q.b	$644$	$2$	644.q	23.c	$11$	$60$	$6$	$5.142$		$_{}$	None	None		$2$	$0$	$0$	$0$	$7$	$-6$			$\mathrm{SU}(2)[C_{11}]$
644.2.t.a	$644$	$2$	644.t	644.t	$22$	$20$	$2$	$5.142$	20.0.$\cdots$.2	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{22}]$	$q+(\beta _{2}+\beta _{13})q^{2}+(-\beta _{10}-\beta _{19})q^{4}+\cdots$
644.2.t.b	$644$	$2$	644.t	644.t	$22$	$20$	$2$	$5.142$	20.0.$\cdots$.2	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{22}]$	$q+(\beta _{2}+\beta _{13})q^{2}+(-\beta _{10}-\beta _{19})q^{4}+\cdots$
644.2.t.c	$644$	$2$	644.t	644.t	$22$	$880$	$88$	$5.142$		$_{}$	None	None		$8$	$0$	$-22$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
644.2.v.a	$644$	$2$	644.v	161.k	$22$	$160$	$16$	$5.142$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
644.2.w.a	$644$	$2$	644.w	92.h	$22$	$360$	$36$	$5.142$		$_{}$	None	None		$2$	$0$	$-1$	$0$	$0$	$-36$			$\mathrm{SU}(2)[C_{22}]$
644.2.w.b	$644$	$2$	644.w	92.h	$22$	$360$	$36$	$5.142$		$_{}$	None	None		$2$	$0$	$-1$	$0$	$0$	$36$			$\mathrm{SU}(2)[C_{22}]$
644.2.y.a	$644$	$2$	644.y	161.m	$33$	$320$	$16$	$5.142$		$_{}$	None	None		$4$	$0$	$0$	$0$	$6$	$-2$			$\mathrm{SU}(2)[C_{33}]$
644.2.z.a	$644$	$2$	644.z	644.z	$66$	$1840$	$92$	$5.142$		$_{}$	None	None		$8$	$0$	$-11$	$0$	$-22$	$0$			$\mathrm{SU}(2)[C_{66}]$
644.2.bc.a	$644$	$2$	644.bc	161.o	$66$	$320$	$16$	$5.142$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{66}]$
644.2.be.a	$644$	$2$	644.be	644.ae	$66$	$1840$	$92$	$5.142$		$_{}$	None	None		$8$	$0$	$-7$	$0$	$-54$	$0$			$\mathrm{SU}(2)[C_{66}]$
644.3.b.a	$644$	$3$	644.b	7.b	$2$	$28$	$28$	$17.548$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-14$			$\mathrm{SU}(2)[C_{2}]$
644.3.g.a	$644$	$3$	644.g	23.b	$2$	$24$	$24$	$17.548$		$_{}$	None	None		$2$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
644.3.l.a	$644$	$3$	644.l	161.f	$6$	$64$	$32$	$17.548$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
644.3.o.a	$644$	$3$	644.o	7.d	$6$	$60$	$30$	$17.548$		$_{}$	None	None		$2$	$0$	$0$	$-6$	$0$	$22$			$\mathrm{SU}(2)[C_{6}]$
644.4.a.a	$644$	$4$	644.a	1.a	$1$	$6$	$6$	$37.997$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-6$	$-10$	$42$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-2-\beta _{1}-\beta _{4})q^{5}+\cdots$
644.4.a.b	$644$	$4$	644.a	1.a	$1$	$6$	$6$	$37.997$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$0$	$-42$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}-7q^{7}+(2+\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$
644.4.a.c	$644$	$4$	644.a	1.a	$1$	$10$	$10$	$37.997$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$10$	$70$	$+$	$2^{9}\cdot 5\cdot 7$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1-\beta _{4})q^{5}+7q^{7}+(12+\beta _{2}+\cdots)q^{9}+\cdots$
644.4.a.d	$644$	$4$	644.a	1.a	$1$	$10$	$10$	$37.997$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$8$	$20$	$-70$	$+$	$2^{9}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(2-\beta _{4})q^{5}-7q^{7}+(12+\cdots)q^{9}+\cdots$
644.4.d.a	$644$	$4$	644.d	161.c	$2$	$48$	$48$	$37.997$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
644.4.i.a	$644$	$4$	644.i	7.c	$3$	$44$	$22$	$37.997$		$_{}$	None	None		$2$	$0$	$0$	$-12$	$-10$	$-38$			$\mathrm{SU}(2)[C_{3}]$
644.4.i.b	$644$	$4$	644.i	7.c	$3$	$44$	$22$	$37.997$		$_{}$	None	None		$2$	$0$	$0$	$12$	$10$	$-6$			$\mathrm{SU}(2)[C_{3}]$
644.4.m.a	$644$	$4$	644.m	161.g	$6$	$96$	$48$	$37.997$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
644.5.b.a	$644$	$5$	644.b	7.b	$2$	$60$	$60$	$66.570$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{2}]$
644.5.g.a	$644$	$5$	644.g	23.b	$2$	$48$	$48$	$66.570$		$_{}$	None	None		$2$	$0$	$0$	$20$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
644.6.a.a	$644$	$6$	644.a	1.a	$1$	$12$	$12$	$103.287$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-25$	$-64$	$-588$	$+$	$2^{13}$	$\mathrm{SU}(2)$	$q+(-2-\beta _{1})q^{3}+(-5+\beta _{5})q^{5}-7^{2}q^{7}+\cdots$
644.6.a.b	$644$	$6$	644.a	1.a	$1$	$12$	$12$	$103.287$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-15$	$-14$	$588$	$+$	$2^{13}\cdot 3^{3}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}+(-1-\beta _{3})q^{5}+7^{2}q^{7}+\cdots$
644.6.a.c	$644$	$6$	644.a	1.a	$1$	$16$	$16$	$103.287$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$-7$	$36$	$-784$	$-$	$2^{19}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(2-\beta _{3})q^{5}-7^{2}q^{7}+(102+\cdots)q^{9}+\cdots$

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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.