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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 104 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
663.1.g.a	$663$	$1$	663.g	663.g	$2$	$1$	$1$	$0.331$	$\Q$	$D_{2}$	$\Q(\sqrt{-51}) $, $\Q(\sqrt{-663}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}-q^{4}+q^{9}+q^{12}+q^{13}+q^{16}+\cdots$
663.1.g.b	$663$	$1$	663.g	663.g	$2$	$1$	$1$	$0.331$	$\Q$	$D_{2}$	$\Q(\sqrt{-51}) $, $\Q(\sqrt{-663}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+q^{3}-q^{4}+q^{9}-q^{12}+q^{13}+q^{16}+\cdots$
663.1.g.c	$663$	$1$	663.g	663.g	$2$	$2$	$2$	$0.331$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-663}) $	None	✓	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-\beta q^{2}-q^{3}+q^{4}+\beta q^{6}-\beta q^{7}+q^{9}+\cdots$
663.1.g.d	$663$	$1$	663.g	663.g	$2$	$2$	$2$	$0.331$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-663}) $	None	✓	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\beta q^{2}+q^{3}+q^{4}-\beta q^{6}+\beta q^{7}+q^{9}+\cdots$
663.1.v.a	$663$	$1$	663.v	663.v	$6$	$2$	$1$	$0.331$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-51}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{4}+(-\zeta_{6}-\zeta_{6}^{2})q^{5}+\cdots$
663.1.v.b	$663$	$1$	663.v	663.v	$6$	$2$	$1$	$0.331$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-51}) $	None		$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{5}+\cdots$
663.1.bb.a	$663$	$1$	663.bb	663.ab	$6$	$2$	$1$	$0.331$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-51}) $	None		$4$	$0$	$0$	$-1$	$-2$	$0$		$1$		$q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-q^{5}+\zeta_{6}^{2}q^{9}+\cdots$
663.1.bb.b	$663$	$1$	663.bb	663.ab	$6$	$2$	$1$	$0.331$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-51}) $	None		$4$	$0$	$0$	$1$	$2$	$0$		$1$		$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+\zeta_{6}^{2}q^{9}+\cdots$
663.2.a.a	$663$	$2$	663.a	1.a	$1$	$1$	$1$	$5.294$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+3q^{8}+\cdots$
663.2.a.b	$663$	$2$	663.a	1.a	$1$	$1$	$1$	$5.294$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{6}-2q^{7}+3q^{8}+\cdots$
663.2.a.c	$663$	$2$	663.a	1.a	$1$	$1$	$1$	$5.294$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$-1$	$-4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-4q^{5}-q^{6}+2q^{7}+\cdots$
663.2.a.d	$663$	$2$	663.a	1.a	$1$	$3$	$3$	$5.294$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$3$	$-6$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
663.2.a.e	$663$	$2$	663.a	1.a	$1$	$3$	$3$	$5.294$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-3$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
663.2.a.f	$663$	$2$	663.a	1.a	$1$	$5$	$5$	$5.294$	5.5.1004368.1	$_{}$	None	None	✓	$1$	$0$	$1$	$-5$	$2$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots$
663.2.a.g	$663$	$2$	663.a	1.a	$1$	$5$	$5$	$5.294$	5.5.153424.1	$_{}$	None	None	✓	$1$	$0$	$3$	$5$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{3})q^{2}+q^{3}+(2+\beta _{3}-\beta _{4})q^{4}+\cdots$
663.2.a.h	$663$	$2$	663.a	1.a	$1$	$6$	$6$	$5.294$	6.6.83831632.1	$_{}$	None	None	✓	$1$	$0$	$2$	$-6$	$0$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
663.2.a.i	$663$	$2$	663.a	1.a	$1$	$6$	$6$	$5.294$	6.6.15187408.1	$_{}$	None	None	✓	$1$	$0$	$4$	$6$	$4$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
663.2.b.a	$663$	$2$	663.b	13.b	$2$	$2$	$2$	$5.294$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+2q^{4}+(1-2\zeta_{6})q^{5}+q^{9}+(-3+\cdots)q^{11}+\cdots$
663.2.b.b	$663$	$2$	663.b	13.b	$2$	$2$	$2$	$5.294$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{3}+q^{4}+iq^{6}-4iq^{7}+\cdots$
663.2.b.c	$663$	$2$	663.b	13.b	$2$	$6$	$6$	$5.294$	6.0.31337472.1	$_{}$	None	None		$2$	$0$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(\beta _{1}-\beta _{5})q^{5}+\cdots$
663.2.b.d	$663$	$2$	663.b	13.b	$2$	$8$	$8$	$5.294$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-8$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}+\beta _{7})q^{2}-q^{3}+(-2+\beta _{5}+\cdots)q^{4}+\cdots$
663.2.b.e	$663$	$2$	663.b	13.b	$2$	$8$	$8$	$5.294$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$8$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
663.2.b.f	$663$	$2$	663.b	13.b	$2$	$10$	$10$	$5.294$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$10$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+q^{3}+(-2+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots$
663.2.e.a	$663$	$2$	663.e	221.b	$2$	$40$	$40$	$5.294$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
663.2.f.a	$663$	$2$	663.f	17.b	$2$	$2$	$2$	$5.294$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+iq^{3}-q^{4}+4iq^{5}+iq^{6}+\cdots$
663.2.f.b	$663$	$2$	663.f	17.b	$2$	$16$	$16$	$5.294$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+\beta _{9}q^{3}+(1-\beta _{5})q^{4}+(\beta _{8}+\cdots)q^{5}+\cdots$
663.2.f.c	$663$	$2$	663.f	17.b	$2$	$18$	$18$	$5.294$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{11}q^{2}-\beta _{7}q^{3}+(2-\beta _{1}+\beta _{10}+\cdots)q^{4}+\cdots$
663.2.i.a	$663$	$2$	663.i	13.c	$3$	$2$	$1$	$5.294$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$-2$	$-1$	$-6$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$
663.2.i.b	$663$	$2$	663.i	13.c	$3$	$2$	$1$	$5.294$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-2$	$1$	$8$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$
663.2.i.c	$663$	$2$	663.i	13.c	$3$	$2$	$1$	$5.294$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-1$	$1$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
663.2.i.d	$663$	$2$	663.i	13.c	$3$	$2$	$1$	$5.294$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$2$	$1$	$4$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$
663.2.i.e	$663$	$2$	663.i	13.c	$3$	$12$	$6$	$5.294$	12.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$2$	$-6$	$8$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1-\beta _{9})q^{3}+(-\beta _{3}-\beta _{8}+\cdots)q^{4}+\cdots$
663.2.i.f	$663$	$2$	663.i	13.c	$3$	$16$	$8$	$5.294$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$8$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{4}+\beta _{7}+\cdots)q^{4}+\cdots$
663.2.i.g	$663$	$2$	663.i	13.c	$3$	$18$	$9$	$5.294$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$1$	$9$	$-10$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+\beta _{12}q^{3}+(-2+\beta _{3}-\beta _{8}+\cdots)q^{4}+\cdots$
663.2.i.h	$663$	$2$	663.i	13.c	$3$	$22$	$11$	$5.294$		$_{}$	None	None		$2$	$0$	$0$	$-11$	$0$	$-3$			$\mathrm{SU}(2)[C_{3}]$
663.2.j.a	$663$	$2$	663.j	17.c	$4$	$32$	$16$	$5.294$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{4}]$
663.2.j.b	$663$	$2$	663.j	17.c	$4$	$40$	$20$	$5.294$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$8$			$\mathrm{SU}(2)[C_{4}]$
663.2.m.a	$663$	$2$	663.m	663.m	$4$	$160$	$80$	$5.294$		$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$-8$			$\mathrm{SU}(2)[C_{4}]$
663.2.n.a	$663$	$2$	663.n	39.f	$4$	$76$	$38$	$5.294$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$-8$			$\mathrm{SU}(2)[C_{4}]$
663.2.n.b	$663$	$2$	663.n	39.f	$4$	$76$	$38$	$5.294$		$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$-8$			$\mathrm{SU}(2)[C_{4}]$
663.2.q.a	$663$	$2$	663.q	663.q	$4$	$8$	$4$	$5.294$	8.0.$\cdots$.9	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{2}+\beta _{6}q^{3}+5\beta _{3}q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots$
663.2.q.b	$663$	$2$	663.q	663.q	$4$	$8$	$4$	$5.294$	8.0.1731891456.1	$_{}$	$\Q(\sqrt{-51}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{4}]$	$q+\beta _{2}q^{3}+2\beta _{5}q^{4}+(-\beta _{1}-\beta _{4}-\beta _{6}+\cdots)q^{5}+\cdots$
663.2.q.c	$663$	$2$	663.q	663.q	$4$	$144$	$72$	$5.294$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
663.2.r.a	$663$	$2$	663.r	663.r	$4$	$160$	$80$	$5.294$		$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
663.2.u.a	$663$	$2$	663.u	221.k	$4$	$80$	$40$	$5.294$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
663.2.w.a	$663$	$2$	663.w	221.l	$6$	$4$	$2$	$5.294$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+2\zeta_{12}^{2}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2+\cdots)q^{4}+\cdots$
663.2.w.b	$663$	$2$	663.w	221.l	$6$	$8$	$4$	$5.294$	$\Q(\zeta_{24})$	$_{}$	None	None		$4$	$0$	$-4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\zeta_{24}^{2}+\zeta_{24}^{4}-\zeta_{24}^{7})q^{2}+\cdots$
663.2.w.c	$663$	$2$	663.w	221.l	$6$	$76$	$38$	$5.294$		$_{}$	None	None		$4$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
663.2.z.a	$663$	$2$	663.z	13.e	$6$	$2$	$1$	$5.294$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+(1-2\zeta_{6})q^{5}+\cdots$
663.2.z.b	$663$	$2$	663.z	13.e	$6$	$4$	$2$	$5.294$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$2$	$1$	$0$	$-2$	$0$	$-12$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(-1+2\beta _{2}+\cdots)q^{5}+\cdots$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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.